非线性科学
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显示 2025年10月21日， 星期二 新的列表
- [1] arXiv:2510.16364 [中文pdf, pdf, html, 其他]
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标题： 多孤子传播和相互作用在$Λ$类EIT介质中的可积方法标题： Multi-Soliton Propagation and Interaction in $Λ$-Type EIT Media: An Integrable Approach评论： 21页，4图，“即将发表于《Photonics》（MDPI）”主题： 模式形成与孤子 (nlin.PS)
电磁诱导透明（EIT）是一种众所周知的量子光学现象，由于跃迁路径之间的量子干涉，使通常不透明的介质变得透明。 本工作研究了由可积Maxwell-Bloch（MB）方程描述的EIT系统中的多孤子动力学，该方程适用于三能级$\Lambda $型原子构型。 通过采用广义规范变换，我们系统地从相应的Lax对中构造出显式的N孤子解。 得到了一、二、三和四孤子解的显式形式并进行了分析。 所得脉冲结构揭示了各种非线性现象，如时间不对称性、能量捕获和孤子相互作用。 它们还突出了相干传播、弹性碰撞和脉冲的部分存储，这些现象在EIT介质中量子记忆、慢光和光子数据传输的设计方面具有潜在的应用价值。 此外，利用激发范数和哈密顿量等基本物理量的守恒，提供了构造的孤子解可积性和稳定性的直接证据。
Electromagnetically induced transparency (EIT) is well known as a quantum optical phenomenon that permits a normally opaque medium to become transparent due to the quantum interference between transition pathways. This work addresses multi-soliton dynamics in an EIT system modeled by the integrable Maxwell-Bloch (MB) equations for a three-level $\Lambda $-type atomic configuration. By employing a generalized gauge transformation, we systematically construct explicit N-soliton solutions from the corresponding Lax pair. Explicit forms of one-, two-, three-, and four-soliton solutions are derived and analyzed. The resulting pulse structures reveal various nonlinear phenomena, such as temporal asymmetry, energy trapping, and soliton interactions. They also highlight coherent propagation, elastic collisions, and partial storage of pulses, which have potential implications for the design of quantum memory, slow light and photonic data transport in EIT media. In addition, the conservation of fundamental physical quantities, such as the excitation norm and Hamiltonian, is used to provide direct evidence of the integrability and stability of the constructed soliton solutions.
- [2] arXiv:2510.16949 [中文pdf, pdf, 其他]
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标题： 我们能多信任混沌吗？ 可预测性的延伸标题： How Far Can We Trust Chaos? Extending the Horizon of PredictabilityAlexandros K. Angelidis, Georgios C. Makris, Evangelos Ioannidis, Ioannis E. Antoniou, Charalampos Bratsas评论： 17页，4图，论文主题： 混沌动力学 (nlin.CD)
混沌揭示了复杂系统科学理解中的一个根本性悖论。 尽管混沌模型在数学上是确定性的，但由于计算机器固有的有限精度，它们在实践中是不可确定的。 在可预测性的界限之外，数值计算会积累误差，这些误差通常难以察觉。 我们研究了生成可靠（无误差）混沌时间序列的可能性。 我们证明，对于两个广泛研究的同构混沌映射，即帐篷映射和逻辑斯蒂映射，这是可行的。 生成的混沌时间序列具有无限的可预测性范围。 获得了一个新的线性公式，用于计算给定精度和可接受误差下逻辑斯蒂映射的可预测性范围。 可靠的（无误差）混沌时间序列作为混沌应用的黄金标准。 我们发现的实际意义包括：(i) 比较预测混沌时间序列的神经网络性能的能力，(ii) 在加密中混沌轨道计算的可靠性和数值准确性，保持高密码强度，以及(iii) 在混沌经济和金融模型中对未来价格的可靠预测。
Chaos reveals a fundamental paradox in the scientific understanding of Complex Systems. Although chaotic models may be mathematically deterministic, they are practically non-determinable due to the finite precision, which is inherent in all computational machines. Beyond the horizon of predictability, numerical computations accumulate errors, often undetectable. We investigate the possibility of reliable (error-free) time series of chaos. We prove that this is feasible for two well-studied isomorphic chaotic maps, namely the Tent map and the Logistic map. The generated chaotic time series have unlimited horizon of predictability. A new linear formula for the horizon of predictability of the Analytic Computation of the Logistic map, for any given precision and acceptable error, is obtained. Reliable (error-free) time series of chaos serve as gold standard for chaos applications. The practical significance of our findings include: (i) the ability to compare the performance of neural networks that predict chaotic time series, (ii) the reliability and numerical accuracy of chaotic orbit computations in encryption, maintaining high cryptographic strength, and (iii) the reliable forecasting of future prices in chaotic economic and financial models.
- [3] arXiv:2510.16999 [中文pdf, pdf, 其他]
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标题： 最外层螺旋磁面的微妙性标题： The subtlety of the outermost stellarator magnetic surface评论： 22页，15图主题： 混沌动力学 (nlin.CD)
用于研究恒星仪中磁力线行为的解析模型，用来研究最外层磁面概念的微妙之处。 我们使用的解析模型有一个由嵌套磁面组成的中心区域。 最外层完全约束的表面具有0.86倍于最外层约束表面的环向通量。 这些表面之间的环形区域中的磁力线会撞击远处的壁，但在这样做之前会在恒星仪的一个周期内经过数万次穿越。 穿越次数如此之多，以至于这个区域可能可以被视为具有约束表面。 在最外层约束表面和一个环向通量为1.02倍的表面之间，磁力线通过四个通量管到达壁上：两个具有向内通量，两个具有向外通量。 其中一对向内-向外通量管是相邻的，而另一对则相隔开。 当环向通量大于最外层约束表面的1.02倍时，大约85%的磁力线在穿越单个周期之前就会撞击壁。 与横向等离子体扩散相比，该区域的等离子体损失速度非常快，因此它们可能与偏滤器的研究无关。 除了从1.02倍约束区域通量内部逃逸的两对向内-向外通量管之外，外部区域还有两对新的向内-向外通量管；一对相邻，另一对相隔开。
An analytic model of the magnetic field line behavior in a stellarator is used to study the subtlety of the concept of an outermost magnetic surface. The analytic model that we use has a central region of nested magnetic surfaces. The outermost perfectly confining surface has a toroidal flux of 0.86 of the toroidal flux of the outermost confining surface. The field lines in the annulus between these surfaces strike a distant wall, but they make tens of thousands of transits through a period of the stellarator before doing so. The number of transits is so large that this region can probably be viewed as having confining surfaces. Between the outermost confining surface and a surface at 1.02 times the toroidal flux field lines go to the walls in four flux tubes: two with inward flux and two with outward flux. One of the inward-outward pairs of flux tubes are adjoining and the other pair is separated. When the toroidal flux is greater than 1.02 of that of the outermost confining surface approximately 85% of the field lines strike the wall before transiting a single period. The loss of plasma from this region is so fast compared to cross-field plasma diffusion that they are probably irrelevant to the study of divertors. In addition to the two inward-outward flux tube pairs that escape from the region inside 1.02 times the flux of the confining region, the outer region has two new inward-outward of flux-tube pairs; one adjoining and one separated.
- [4] arXiv:2510.17031 [中文pdf, pdf, html, 其他]
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标题： 修改的开放Toda链和准可积性标题： Modified open Toda chain and quasi-integrability评论： 16页，LaTeX，4个图表主题： 精确可解与可积系统 (nlin.SI) ; 数学物理 (math-ph)
我们研究了三粒子开放Toda链的准可积变形，该变形通过引入一个平移不变的三体相互作用项来构建。 尽管这种修改显式地破坏了标准Toda模型的精确可积性，但它保留了基本的结构特性，包括能量和动量守恒。 此外，我们证明在特定的时间反演和链坐标之间的离散对称性下，系统具有准守恒的高阶积分。 通过分析变形动力学的解析和数值分析，我们展示了准守恒量的出现及其长时间的持续存在，从而在最小的非线性链中建立了准可积性的受控实现。 鉴于可积系统在阐明经典和量子模型动力学中的核心作用，这个框架提供了一个具体的环境来研究可积性逐渐破坏以及准可积性在少体系统中出现的机制。
We present a study of a quasi-integrable deformation of the three-particle open Toda chain, constructed by introducing a translation-invariant three-body interaction terms. Although this modification explicitly breaks the exact integrability of the standard Toda model, it retains fundamental structural properties, including energy and momentum conservation. Furthermore, we show that under a specific time-reflection and discrete symmetry among the chain coordinates, the system admits a quasi-conserved higher-order integral. Through analytic and numerical analysis of the deformed dynamics, we demonstrate the emergence and long-time persistence of quasi-conserved quantities, thereby establishing a controlled realization of quasi-integrability in a minimal nonlinear chain. Given the central role of integrable systems in elucidating the dynamics of classical and quantum models, this framework provides a concrete setting to investigate the mechanisms underlying the gradual breakdown of integrability and the onset of quasi-integrability in few-body systems.
新提交 (展示 4 之 4 条目 )
- [5] arXiv:2510.16038 (交叉列表自 cond-mat.mes-hall) [中文pdf, pdf, html, 其他]
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标题： 激光场驱动下高度有序硅纳米线阵列的本征最大光吸收标题： Intrinsic Maximum Light Absorption in Laser-Field-Driven Growth of Highly Ordered Silicon Nanowire Arrays评论： 4幅图，12页主题： 中尺度与纳米尺度物理 (cond-mat.mes-hall) ; 适应性与自组织系统 (nlin.AO)
我们提供了非平衡系统中状态选择原理的直接实验证据。 使用激光驱动的硅纳米线生长作为一个独特干净且可量化的平台，我们表明，作为系统自发选择最大化其集体光吸收的周期性的结果，长程有序阵列出现。 这建立了一个最大耗散/吸收原理与涌现结构秩序之间的直接可测量联系。 因此，我们的结果为非平衡自组织模型提供了一个具体的测试。
We provide direct experimental evidence for a state-selection principle in a far-from-equilibrium system. Using the laser-driven growth of silicon nanowires as a uniquely clean and quantifiable platform, we show that a long-range ordered array emerges as the system spontaneously selects the periodicity that maximizes its collective light absorption. This establishes a direct, measurable link between a maximum dissipation/absorption principle and emergent structural order. Our results thus offer a concrete test for models of non-equilibrium self-organization.
- [6] arXiv:2510.16312 (交叉列表自 physics.soc-ph) [中文pdf, pdf, 其他]
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标题： 复杂系统的可预测性标题： Predictability of Complex Systems主题： 物理与社会 (physics.soc-ph) ; 图形学 (cs.GR) ; 信息论 (cs.IT) ; 系统与控制 (eess.SY) ; 数学物理 (math-ph) ; 适应性与自组织系统 (nlin.AO)
复杂系统的研究已经引起了自然科学、社会科学和工程领域研究人员的广泛关注。预测是该领域中的核心问题之一。尽管大多数相关研究都集中在预测方法上，但对复杂系统可预测性的研究正逐渐受到跨学科的关注，旨在提供理论和工具来解决一个关键问题：预测精度的极限是什么？可预测性本身可以作为表征复杂系统的重要特征，准确估计可预测性可以为预测算法的研究提供基准。这使研究人员能够清楚地识别当前预测精度与理论极限之间的差距，从而帮助他们确定现有算法是否仍有显著的改进空间。更重要的是，研究可预测性通常需要开发新的理论和方法，这可以进一步激发更有效算法的设计。在过去的几十年里，这一领域经历了显著的发展。特别是数据科学的快速发展，引入了大量数据驱动的方法来理解和量化可预测性。本综述总结了代表性成果，整合了数据驱动和机制性的视角。在简要介绍关注主题的重要性后，我们将探讨三个核心方面：时间序列的可预测性、网络结构的可预测性以及动态过程的可预测性。最后，我们将提供各种领域的广泛应用实例，并概述未来研究的开放性挑战。
The study of complex systems has attracted widespread attention from researchers in the fields of natural sciences, social sciences, and engineering. Prediction is one of the central issues in this field. Although most related studies have focused on prediction methods, research on the predictability of complex systems has received increasing attention across disciplines--aiming to provide theories and tools to address a key question: What are the limits of prediction accuracy? Predictability itself can serve as an important feature for characterizing complex systems, and accurate estimation of predictability can provide a benchmark for the study of prediction algorithms. This allows researchers to clearly identify the gap between current prediction accuracy and theoretical limits, thereby helping them determine whether there is still significant room to improve existing algorithms. More importantly, investigating predictability often requires the development of new theories and methods, which can further inspire the design of more effective algorithms. Over the past few decades, this field has undergone significant evolution. In particular, the rapid development of data science has introduced a wealth of data-driven approaches for understanding and quantifying predictability. This review summarizes representative achievements, integrating both data-driven and mechanistic perspectives. After a brief introduction to the significance of the topic in focus, we will explore three core aspects: the predictability of time series, the predictability of network structures, and the predictability of dynamical processes. Finally, we will provide extensive application examples across various fields and outline open challenges for future research.
- [7] arXiv:2510.16766 (交叉列表自 math.OC) [中文pdf, pdf, html, 其他]
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标题： 弱耦合振荡器系统的加法和参数固定控制协议的等价性标题： Equivalence of additive and parametric pinning control protocols for systems of weakly coupled oscillators评论： 会议论文（提交至SICE 2026）主题： 优化与控制 (math.OC) ; 适应性与自组织系统 (nlin.AO) ; 模式形成与孤子 (nlin.PS) ; 计算物理 (physics.comp-ph)
在控制理论中，控制网络上的非线性系统的行为是一项关键任务，特别是同步控制，由于其广泛的应用性。 在本工作中，我们关注的是固定控制，并研究了两种不同的方法：第一种方法在工程应用中更为常见，其中通过外部输入实现控制（加法固定）；另一种方法则是改变固定节点的参数（参数固定）。 通过相位约简技术，我们表明对于表现出周期振荡行为的弱耦合系统，这两种固定方法是等效的。 通过数值模拟，我们验证了对耦合Stuart--Landau振子系统的这一说法。 我们的结果为固定控制在现实世界系统中的进一步应用铺平了道路。
Controlling the behavior of nonlinear systems on networks is a paramount task in control theory, in particular the control of synchronization, given its vast applicability. In this work, we focus on pinning control and we examine two different approaches: the first, more common in engineering applications, where the control is implemented through an external input (additive pinning); the other, where the parameters of the pinned nodes are varied (parametric pinning). By means of the phase reduction technique, we show that the two pinning approaches are equivalent for weakly coupled systems exhibiting periodic oscillatory behaviors. Through numerical simulations, we validate the claim for a system of coupled Stuart--Landau oscillators. Our results pave the way for further applications of pinning control in real-world systems.
- [8] arXiv:2510.16808 (交叉列表自 physics.soc-ph) [中文pdf, pdf, html, 其他]
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标题： 将康多塞陪审团定理推广到社交网络标题： Generalizing Condorcet's Jury Theorem to Social Networks评论： 15页主题： 物理与社会 (physics.soc-ph) ; 适应性与自组织系统 (nlin.AO)
我们将康多塞陪审团定理（CJT）推广到社会连接的人口，其中代理人在存在狂热者的情况下在网络中修改离散选择。 自由代理接收关于正确替代方案的私人信息信号，并在每次更新时，保留其状态或模仿一个随机选择的邻居（自由或狂热者）。 对于有限网络，我们推导出投票数的显式稳态定律，并表征当自由选民数量趋于无穷大时相应的投票份额极限。 对于多数规则——无论是二元还是多替代设置——我们通过正则化不完全β函数得到了精确的准确性极限。 对于多数规则，我们建立了准确性上的尖锐显式下界，用正则化不完全β函数表示。 在正确替代方案的绝对多数条件下，多数和多数准确性都严格超过任何单个选民的准确性，表明通过社会互动耦合的信息信号在群体层面被放大。 这些结果将CJT扩展到独立性之外，并为社会、生物和工程环境中的联网决策系统提供了显式准确性基准。
We generalize Condorcet's jury theorem (CJT) to socially connected populations in which agents revise discrete choices on a network in the presence of zealots. Free agents receive privately informative signals about the correct alternative and, at each update, either retain their state or imitate a uniformly chosen neighbor (free or zealot). For finite networks, we derive closed-form stationary laws for vote counts, and we characterize the corresponding vote-share limits as the number of free voters tends to infinity. For majority rule -- both in binary and multi-alternative settings -- we obtain an exact accuracy limit in closed form via the regularized incomplete beta function. For plurality rule, we establish sharp closed-form lower bounds on accuracy, expressed in terms of regularized incomplete beta functions. Under an absolute-majority condition for the correct alternative, both majority and plurality accuracies strictly exceed the accuracy of any single voter, showing that informative signals, coupled through social interaction, are amplified at the group level. These results extend CJT beyond independence and provide closed-form accuracy benchmarks for networked decision systems in social, biological, and engineered settings.
- [9] arXiv:2510.17016 (交叉列表自 q-bio.PE) [中文pdf, pdf, html, 其他]
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标题： 伏击策略影响石头剪刀布模型中物种的主导性和共存标题： Ambush strategy impacts species predominance and coexistence in rock-paper-scissors models评论： 7页，6图主题： 种群与进化 (q-bio.PE) ; 适应性与自组织系统 (nlin.AO) ; 模式形成与孤子 (nlin.PS) ; 应用物理 (physics.app-ph) ; 生物物理 (physics.bio-ph)
我们研究了在遵循空间石头剪刀布游戏规则的循环模型中自适应伏击策略。 在我们的模型中，某一物种的个体具有认知能力来感知环境线索，并评估在争夺自然资源的空间竞争中它们所支配物种的局部密度。 基于这种评估，它们要么发起直接攻击，要么如果目标个体的局部浓度不足以证明风险合理，则战略性地重新定位以准备伏击。 为了量化这些行为策略的进化后果，我们进行随机模拟，分析出现的空间模式以及物种密度对个体用于决定立即攻击或预期的阈值的依赖性。 我们的发现表明，尽管这些认知策略旨在提高效率，但由于循环支配的限制，它们可能会减少物种的丰富度。 我们确定了一个最佳决策阈值：仅当目标个体的局部密度超过15%时才进行攻击，这在选择风险和长期持续性之间提供了最佳平衡。 此外，伏击策略有利于低移动性的生物，将共存概率提高多达53%。 这些结果加深了对空间生态学中自适应决策的理解，将认知复杂性与生态系统弹性及灭绝风险联系起来。
We investigate the adaptive Ambush strategy in cyclic models following the rules of the spatial rock-paper-scissors game. In our model, individuals of one species possess cognitive abilities to perceive environmental cues and assess the local density of the species they dominate in the spatial competition for natural resources. Based on this assessment, they either initiate a direct attack or, if the local concentration of target individuals does not justify the risk, reposition strategically to prepare an ambush. To quantify the evolutionary consequences of these behavioural strategies, we perform stochastic simulations, analysing emergent spatial patterns and the dependence of species densities on the threshold used by individuals to decide between immediate attack or anticipation. Our findings reveal that, despite being designed to enhance efficiency, cognitive strategies can reduce the abundance of the species due to the constraints of cyclic dominance. We identify an optimal decision threshold: attacking only when the local density of target individuals exceeds 15% provides the best balance between selection risk and long-term persistence. Furthermore, the Ambush strategy benefits low-mobility organisms, increasing coexistence probabilities by up to 53%. These results deepen the understanding of adaptive decision-making in spatial ecology, linking cognitive complexity to ecosystem resilience and extinction risk.
- [10] arXiv:2510.17428 (交叉列表自 cond-mat.stat-mech) [中文pdf, pdf, html, 其他]
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标题： 一维冷气体中的流体力学分解标题： Breakdown of hydrodynamics in a one-dimensional cold gas评论： 5页，4图主题： 统计力学 (cond-mat.stat-mech) ; 混沌动力学 (nlin.CD)
以下模型被进行分析和数值研究：质量为$m,\mu,m, \dots$($m\geq\mu$) 的点粒子分布在正半轴上。 它们的动力学由给位于原点的粒子一个正速度来启动；在过程中粒子之间发生弹性碰撞。 我们证明，对于某些$m/\mu$的值，从粒子等距分布的初始状态开始，系统以流体动力学方式演化：(i) 最右边的粒子（冲击波前沿）按照$t^{\delta}$以$\delta < 1$运动；(ii) 前沿之后被反弹的粒子进入负半轴；(iii) 飞溅——即位置为$x\leq 0$的粒子——以弹道方式运动，并最终接管整个系统的能量。 这些结果与 S. Chakraborti 等人，在 SciPost Phys. 2022, 13, 074 中得到的结果一致，适用于$m/\mu=2$和随机初始粒子位置。 同时，我们明确找到了正数集合$\{\mathcal{M}_i, i \in \mathbf{N} \}$，使得对于$m/\mu = \mathcal{M}_i$，$i\leq 700$，以下成立：(a) 没有飞溅；(b) 同时移动的粒子数量最多为三个；(c) 冲击前沿以弹道方式移动。然而，如果像 S. Chakraborti 等人那样，粒子位置是从均匀分布的集合中采样的，那么对于$m/\mu = \mathcal{M}_i$，系统将以流体动力学方式演化。
The following model is studied analytically and numerically: point particles with masses $m,\mu,m, \dots$ ($m\geq\mu$) are distributed over the positive half-axis. Their dynamics is initiated by giving a positive velocity to the particle located at the origin; in its course the particles undergo elastic collisions. We show that, for certain values of $m/\mu$, starting from the initial state where the particles are equidistant the system evolves in a hydrodynamic way: (i) the rightmost particle (blast front) moves as $t^{\delta}$ with $\delta < 1$; (ii) recoiled particles behind the front enter the negative half-axis; (iii) the splatter -- the particles with locations $x\leq 0$ -- moves in the ballistic way and eventually takes over the whole energy of the system. These results agree with those obtained in S. Chakraborti et al, SciPost Phys. 2022, 13, 074, for $m/\mu=2$ and random initial particle positions. At the same time, we explicitly found the collection of positive numbers $\{\mathcal{M}_i, i \in \mathbf{N} \}$ such that, for $m/\mu = \mathcal{M}_i$, $i\leq 700$, the following holds: (a) the splatter is absent; (b) the number of simultaneously moving particles is at most three; (c) the blast front moves in the ballistic way. However, if, similarly as in S. Chakraborti et al, the particle positions are sampled from a uniformly distributed ensemble, for $m/\mu = \mathcal{M}_i$ the system evolves in a hydrodynamic way.
- [11] arXiv:2510.17492 (交叉列表自 q-bio.NC) [中文pdf, pdf, html, 其他]
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标题： 无强外部电流下的自维持平衡状态理论标题： A theory for self-sustained balanced states in absence of strong external currents主题： 神经与认知 (q-bio.NC) ; 混沌动力学 (nlin.CD) ; 生物物理 (physics.bio-ph)
具有平衡兴奋和抑制的循环神经网络表现出不规则的异步动力学，这对于皮层计算是基本的。 经典平衡机制需要强烈的外部输入来维持有限的放电率，这引发了对其生物学合理性的担忧。 在这里，我们研究了一种基于短时突触抑制（STD）的替代机制，该机制作用于兴奋性-兴奋性突触，能够在不需要外部输入的情况下动态平衡网络活动。 通过使用数值模拟和理论研究，我们表征了一个由$N$速率神经元模型组成的大量耦合网络的动力学。 根据突触强度$J_0$，网络表现出两种不同的状态：在足够小的$J_0$时，它收敛到一个均匀的固定点，而在足够大的$J_0$时，它表现出速率混沌。 对于有限的网络，我们观察到几种不同的通向混沌的路径，这取决于网络的实现方式。 分离均匀稳定解与速率混沌的过渡区域的宽度似乎随着$N$的增加而缩小，并最终在热力学极限中消失。 通过采用动力学平均场方法对速率混沌状态进行表征，一方面使我们确认这种新的平衡机制能够在热力学极限下维持有限的不规则活动，另一方面揭示了平衡是通过动态抵消由大量耦合产生的输入相关性来实现的。 我们的发现表明，STD为平衡网络提供了一种内在的自我调节机制，在不需要生物上不现实的输入的情况下维持不规则但稳定的活动。 这项工作扩展了平衡网络范式，提供了关于皮层电路如何通过突触适应保持鲁棒动力学的见解。
Recurrent neural networks with balanced excitation and inhibition exhibit irregular asynchronous dynamics, which is fundamental for cortical computations. Classical balance mechanisms require strong external inputs to sustain finite firing rates, raising concerns about their biological plausibility. Here, we investigate an alternative mechanism based on short-term synaptic depression (STD) acting on excitatory-excitatory synapses, which dynamically balances the network activity without the need of external inputs. By employing numerical simulations and theoretical investigations we characterize the dynamics of a massively coupled network made up of $N$ rate-neuron models. Depending on the synaptic strength $J_0$, the network exhibits two distinct regimes: at sufficiently small $J_0$, it converges to a homogeneous fixed point, while for sufficiently large $J_0$, it exhibits Rate Chaos. For finite networks, we observe several different routes to chaos depending on the network realization. The width of the transition region separating the homogeneous stable solution from Rate Chaos appears to shrink for increasing $N$ and eventually to vanish in the thermodynamic limit. The characterization of the Rate Chaos regime performed by employing Dynamical Mean Field approaches allow us on one side to confirm that this novel balancing mechanism is able to sustain finite irregular activity even in the thermodynamic limit, and on the other side to reveal that the balancing occurs via dynamic cancellation of the input correlations generated by the massive coupling. Our findings show that STD provides an intrinsic self-regulating mechanism for balanced networks, sustaining irregular yet stable activity without the need of biologically unrealistic inputs. This work extends the balanced network paradigm, offering insights into how cortical circuits could maintain robust dynamics via synaptic adaptation.
交叉提交 (展示 7 之 7 条目 )
- [12] arXiv:2203.13222 (替换) [中文pdf, pdf, html, 其他]
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标题： 基于混合动力系统中高阶横向不连续映射的改进稳定性估计和飞行时间预测标题： Improved Stability Estimates and Flight Time Predictions Using Higher-Order Transverse Discontinuity Mapping in Hybrid Dynamical Systems评论： 41页，19图主题： 混沌动力学 (nlin.CD)
本文强调了在混合动力系统中，由一阶横向不连续映射（TDM）获得的动力学估计与直接数值观测之间存在的不一致之处。 展示了在不连续边界附近对混合非线性动力系统进行局部线性化时的陷阱，并举例说明这种线性化可能导致对与刚性障碍物的横向相互作用中碰撞发生的错误估计。 提出了一种高阶TDM以克服这一缺陷，从而能够更准确地分析碰撞发生时间、状态转换，以及轨迹的演化。 在不连续边界附近的局部邻域内，两条紧密启动的轨迹的飞行时间差异被估计到$\mathcal{O}(2)$。 由此得到的二次方程表明，对应于负判别式的撞击状态附近的轨道不会到达不连续边界。 此外，TDM解析表达式中的$\mathcal{O}(2)$修正项确保了在接近擦除的低速碰撞情况下，飞行时间估计不会发散，从而避免对映射状态的高估。 随后开发了一种数值方法，用于估计包含所提出的高阶TDM的跳跃矩阵，以避免错误的碰撞发生。 提出了对现有用于数值量化局部稳定性的算法的修改，即李雅普诺夫谱和弗洛凯乘子。 使用所提出的高阶方法对硬碰撞振子和一对碰撞振子的代表性情况进行稳定性分析，结果与数值获得的分岔图一致。
This article emphasizes on inconsistencies in the dynamical estimates obtained by first-order transverse discontinuity mapping (TDM) and direct numerical observations for hybrid dynamical systems. Pitfalls of locally linearizing hybrid nonlinear dynamical systems near discontinuity boundaries are demonstrated along with examples of how such linearization could lead to incorrect estimates of impact occurrences for transverse interactions with a rigid barrier. A higher-order TDM is proposed to overcome this shortcoming, allowing for better analytical estimation of impact occurrence times, state transitions, and, consequently, the evolution of trajectories. The difference in flight times of two closely initiated trajectories in the local neighbourhood of a discontinuity boundary is estimated up to $\mathcal{O}(2)$. The resulting quadratic equation implies that the orbits local to the impacting state, corresponding to a negative discriminant, won't reach the discontinuity boundary. Further, the $\mathcal{O}(2)$ correction terms to the analytical expression of the TDM ensure that the flight time estimates do not diverge for low-velocity impacts near grazing, thereby avoiding overestimation of the mapped state. A numerical method is subsequently developed to estimate a saltation matrix incorporating the proposed higher-order TDM to avoid incorrect impact occurrences. Modifications to the existing algorithms used to numerically quantify local stability, namely the Lyapunov spectra and Floquet multipliers, are proposed. Stability analyses using the proposed higher-order approach are carried out for representative cases of a hard impact oscillator and a pair impact oscillator, with results consistent with numerically obtained bifurcation diagrams.
- [13] arXiv:2507.22643 (替换) [中文pdf, pdf, html, 其他]
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标题： 熵与聚类分析混沌漫游现象标题： Analysis of the Chaotic Itinerancy Phenomenon using Entropy and Clustering评论： 27页，6表，14图主题： 混沌动力学 (nlin.CD) ; 动力系统 (math.DS)
我们引入了一种新的方法，利用熵的概念和聚类算法来分析动态系统中的混沌漫游现象。 我们通过局部香农熵和局部排列熵来确定可能发生混沌漫游的系统。 在这些系统中，我们使用基于密度的聚类算法找到准稳定状态（吸引子残骸）和混沌过渡状态。 然后，我们的方法专注于通过这些状态内的驻留时间和它们之间的混沌过渡的表征，借助一些统计检验来研究混沌漫游动力学。 我们在全局耦合逻辑斯蒂映射（GCM）系统上展示了这些方法的有效性，这是一个众所周知的表现出混沌漫游的模型。 特别是，我们在GCM系统中对大量参数进行了全面计算，并通过算法识别出Kaneko在数值模拟中观察到的相干和间歇相作为漫游动力学。
We introduce a new methodology for the analysis of the phenomenon of chaotic itinerancy in a dynamical system using the notion of entropy and a clustering algorithm. We determine systems likely to experience chaotic itinerancy by means of local Shannon entropy and local permutation entropy. In such systems, we find quasi-stable states (attractor ruins) and chaotic transition states using a density-based clustering algorithm. Our approach then focuses on examining the chaotic itinerancy dynamics through the characterization of residence times within these states and chaotic transitions between them with the help of some statistical tests. We demonstrate the effectiveness of these methods on the system of globally coupled logistic maps (GCM), a well-known model exhibiting chaotic itinerancy. In particular, we conduct comprehensive computations for a large number of parameters in the GCM system and algorithmically identify itinerant dynamics observed previously by Kaneko in numerical simulations as coherent and intermittent phases.
- [14] arXiv:2508.12808 (替换) [中文pdf, pdf, html, 其他]
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标题： 针对特定目标的视觉神经启发图像修复方法标题： Visual-Neural-Inspired Image Inpainting for Specific Objects-of-Interest Imaging主题： 模式形成与孤子 (nlin.PS)
传统图像修复技术通常处理整个图像，这往往导致计算效率低下和信息冗余的易感性，尤其是在被遮挡或杂乱的场景中。 受皮层处理机制的启发，本研究引入了一种称为“特定目标成像”（SIOI）的新框架，以克服这些限制。 所提出的方法首先从复杂场景中提取并编码对象级表示，生成可以无缝集成到现有修复流程中的结构和语义先验。 在专用目标数据集——茶壶、大象、长颈鹿和斑马上的广泛评估表明，包含SIOI的模型在SSIM、PSNR、MAE和LPIPS等关键指标上始终优于不包含SIOI的模型。 该框架在低光照、高噪声、多个目标遮挡和运动模糊等挑战性条件下也表现出强大的鲁棒性。 此外，基于认知神经科学的理论分析揭示了“以目标为先”的感知机制与视觉皮层区域（V1-V4）动态特征调制之间的有意义联系。 通过显著增强各种修复模型中的目标一致性和语义连贯性，这项工作不仅推进了高效且目标感知的图像修复，还促进了脑启发计算与前沿修复技术之间的跨学科融合。
Conventional image inpainting techniques typically process entire images, which often leads to computational inefficiency and susceptibility to information redundancy, particularly in occluded or cluttered scenes. Inspired by cortical processing mechanisms, this study introduces a novel framework termed "Specific Object-of-Interest Imaging" (SIOI) to overcome these limitations. The proposed approach first extracts and encodes object-level representations from complex scenes, producing structural and semantic priors that can be seamlessly integrated into existing inpainting pipelines. Extensive evaluations on dedicated object datasets--Teapot, Elephant, Giraffe, and Zebra--demonstrate that models incorporating SIOI consistently outperform those without it across key metrics including SSIM, PSNR, MAE, and LPIPS. The framework also exhibits strong robustness under challenging conditions such as low illumination, high noise, multiple object occlusions, and motion blur. Furthermore, theoretical analysis grounded in cognitive neuroscience reveals meaningful connections between the "object-first" perceptual mechanism and dynamic feature modulation in visual cortical areas (V1-V4). By significantly enhancing object consistency and semantic coherence across diverse inpainting models, this work not only advances efficient and target-aware image restoration but also fosters interdisciplinary convergence between brain-inspired computation and cutting-edge inpainting technologies.
- [15] arXiv:2502.20614 (替换) [中文pdf, pdf, html, 其他]
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标题： 复化 Kuramoto 模型中的同步标题： Synchronization in the complexified Kuramoto model评论： arXiv管理员注释：与arXiv:2309.01893存在大量文本重叠主题： 动力系统 (math.DS) ; 混沌动力学 (nlin.CD)
在本文中，我们考虑一个$N$-振荡器复化 Kuramoto 模型。 我们首先观察到在所有耦合范围内存在表现出有限时间爆破行为的解。 当耦合强度$\lambda>\lambda_c$时，为一般$N \geq 2$的各种类型的同步建立了充分条件。 另一方面，我们分析了耦合强度较弱的情况。 对于$N=2$耦合低于$\lambda_c$的情况，我们的复分析方法不仅恢复了 Thümler--Srinivas--Schröder--Timme 报告的周期轨道，还首次提供了它们的精确周期$T_{\omega,\lambda}=2\pi/\sqrt{\omega^{2}-\lambda^{2}}$，确认了完全相位锁定。 此外，对于临界情况$\lambda = \lambda_c$，我们发现复化 Kuramoto 系统存在同宿轨道。 这些现象显著地区分了复化 Kuramoto 模型与实数 Kuramoto 系统，因为在后者的系统中，当$\lambda<\lambda_c$时同步永远不会发生。 对于$N=3$，我们证明如果自然频率呈等差数列，即使耦合强度较弱，也可以通过某些初始条件实现非平凡的同步状态。 特别是，我们表征了临界耦合强度 ($\lambda/\lambda_c = 0.85218915...$)，使得实数 Kuramoto 模型中的半稳定平衡点分叉为一对稳定和不稳定平衡点，在复化 Kuramoto 模型中标志着一种新的现象。
In this paper, we consider an $N$-oscillators complexified Kuramoto model. We first observe that there are solutions exhibiting finite-time blow-up behavior in all coupling regimes. When the coupling strength $\lambda>\lambda_c$, sufficient conditions for various types of synchronization are established for general $N \geq 2$. On the other hand, we analyze the case when the coupling strength is weak. For $N=2$ with coupling below $\lambda_c$, our complex-analytic approach not only recovers the periodic orbits reported by Th\"umler--Srinivas--Schr\"oder--Timme but also provides, for the first time, their exact period $T_{\omega,\lambda}=2\pi/\sqrt{\omega^{2}-\lambda^{2}}$, confirming full phase locking. Furthermore, for the critical case $\lambda = \lambda_c$, we find that the complexified Kuramoto system admits homoclinic orbits. These phenomena significantly differentiate the complexified Kuramoto model from the real Kuramoto system, as synchronization never occurs when $\lambda<\lambda_c$ in the latter. For $N=3$, we demonstrate that if the natural frequencies are in arithmetic progression, non-trivial synchronization states can be achieved for certain initial conditions even when the coupling strength is weak. In particular, we characterize the critical coupling strength ($\lambda/\lambda_c = 0.85218915...$) such that a semistable equilibrium point in the real Kuramoto model bifurcates into a pair of stable and unstable equilibria, marking a new phenomenon in complexified Kuramoto models.
- [16] arXiv:2505.09254 (替换) [中文pdf, pdf, html, 其他]
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标题： 迈向具有信息性和可操作性的社交媒体研究标题： Moving towards informative and actionable social media researchJoseph B. Bak-Coleman, Stephan Lewandowsky, Philipp Lorenz-Spreen, Arvind Narayanan, Amy Orben, Lisa Oswald主题： 社会与信息网络 (cs.SI) ; 适应性与自组织系统 (nlin.AO)
社交媒体在现代生活中几乎无处不在，引发了对其社会影响的担忧——从心理健康和两极分化到暴力和民主破坏。 然而，关于其因果效应的研究结果仍然不明确：观察性研究通常发现令人担忧的关联，而随机对照试验（RCT）往往得出小规模、冲突或无效的结果。 文献综述往往优先考虑来自RCT的因果结论，常认为对社交媒体的担忧被夸大了。 然而，与观察性研究一样，RCT也依赖于在社交媒体背景下很容易被违反的假设，尤其是在大规模社会结果方面。 在此，我们列举并探讨社交媒体作为复杂系统的特征，这些特征挑战了我们在社会规模上推断因果关系的能力。 借鉴曾面临类似挑战的学科（如气候科学或流行病学）的见解，我们提出了一条前进的道路，结合观察性和实验性方法的优势，同时承认各自局限性。
Social media is nearly ubiquitous in modern life, raising concerns about its societal impacts-from mental health and polarization to violence and democratic disruption. Yet research on its causal effects remains inconclusive: observational studies often find concerning associations, while randomized controlled trials (RCTs) tend to yield small, conflicting, or null results. Literature summaries tend to causally prioritize findings from RCTs, often arguing that concerns about social media are overstated. However, like observational studies, RCTs rely on assumptions that can easily be violated in the context of social media, especially regarding societal outcomes at scale. Here, we enumerate and examine the features of social media as a complex system that challenge our ability to infer causality at societal scales. Drawing on insight from disciplines that have faced similar challenges, like climate-science or epidemiology, we propose a path forward that combines the strength of observational and experimental approaches while acknowledging the limitations of each.
- [17] arXiv:2507.20484 (替换) [中文pdf, pdf, html, 其他]
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标题： 扁平化轴子势能的暗光子暗物质标题： Dark photon dark matter from flattened axion potentialsHong-Yi Zhang, Paola Arias, Andrew Cheek, Enrico D. Schiappacasse, Luca Visinelli, Leszek Roszkowski评论： 13页，8图；已接受版本主题： 高能物理 - 现象学 (hep-ph) ; 宇宙学与非星系天体物理学 (astro-ph.CO) ; 模式形成与孤子 (nlin.PS)
暗光子可以通过与振荡轴子场的耦合在早期宇宙中被共振产生。 然而，这种机制通常需要大的轴子-暗光子耦合或一定程度的微调。 在这项工作中，我们提出了一种新情景，在这种情景中，暗光子的高效产生来自于轴子势在大场值处比二次方更浅的情况。 对于中等大的初始错位角，轴子场的振荡可以通过参数共振触发高效的暗光子产生或强烈的轴子自共振。 当自共振占主导并破坏场的均匀性时，我们表明孤立子——局部的、振荡的轴子场配置——自然形成，并且可以在耦合为$\gtrsim \mathcal O(1)$的情况下持续产生暗光子。 对于暗光子质量不超过轴子质量三个数量级的情况，产生的暗光子可以占现今暗物质的重要部分。 我们通过一个基准模型的数值晶格模拟支持这一情景。 我们的结果进一步激发了对超轻暗光子暗物质的实验搜索。 模拟代码可在 https://github.com/hongyi18/AxionDarkPhotonSimulator 公开获取。
Dark photons can be resonantly produced in the early universe via their coupling to an oscillating axion field. However, this mechanism typically requires large axion--dark photon couplings or some degree of fine-tuning. In this work, we present a new scenario in which efficient dark photon production arises from axion potentials that are shallower than quadratic at large field values. For moderately large initial misalignment angles, the oscillation of the axion field can trigger either efficient dark photon production or strong axion self-resonance via parametric resonance. When self-resonance dominates and disrupts the field's homogeneity, we show that oscillons -- localized, oscillating axion field configurations -- naturally form and can sustain continued dark photon production, provided the coupling is $\gtrsim \mathcal O(1)$. For dark photon mass up to three orders of magnitude below the axion mass, the produced dark photons can account for a significant fraction of the present-day dark matter. We support this scenario with numerical lattice simulations of a benchmark model. Our results further motivate experimental searches for ultralight dark photon dark matter. The simulation code is publicly available at https://github.com/hongyi18/AxionDarkPhotonSimulator.
- [18] arXiv:2510.09832 (替换) [中文pdf, pdf, html, 其他]
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标题： 自旋轨道耦合的自旋-1玻色-爱因斯坦凝聚体中的稳定高阶涡旋标题： Stable High-Order Vortices in Spin-Orbit-Coupled Spin-1 Bose-Einstein Condensates评论： 将发表在《物理评论A》上主题： 量子气体 (cond-mat.quant-gas) ; 模式形成与孤子 (nlin.PS)
本文贡献探讨了在梯度磁场作用下，具有自旋-轨道耦合（SOC）的自旋-1玻色-爱因斯坦凝聚体（BECs）基态（GS）中发生的相变。通过以精确方式求解相应的线性化系统，我们确定了GS相变发生的条件，从而将激发态转化为GS。对包括密度-密度和自旋-自旋相互作用在内的完整非线性系统的数值分析进行了研究。对于排斥型自旋-自旋相互作用，结果类似于线性情况，而吸引型自旋-自旋相互作用导致在GS相变点附近形成混合态。此外，发现高阶涡旋孤子即使在非线性区域也保持稳定。这些发现表明，任意的绕数可以对应于稳定的GS，从而有助于理解SOC BECs中的拓扑性质。
The present contribution explores phase transitions that occur in the ground state (GS) of spin-1 Bose-Einstein condensates (BECs) with spin-orbit coupling (SOC) under the action of gradient magnetic fields. By solving the corresponding linearized system in an exact fashion, we identify the conditions under which the GS phase transitions occur, thus transforming excited states into GS. The study of the full nonlinear system, including both density-density and spin-spin interactions, is numerically analyzed. For the case of repulsive spin-spin interactions, the results resemble the linear case, while attractive spin-spin interactions lead to the formation of mixed-states near the GS phase-transition points. Additionally, higher-order vortex solitons are found to be stable even in the nonlinear regime. These findings demonstrate that arbitrary winding numbers can be achieved as corresponding to stable GS and thus contributing to the understanding of topological properties in SOC BECs.
- [19] arXiv:2510.10381 (替换) [中文pdf, pdf, html, 其他]
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标题： 使用平均信息增益量化基于代理的模型中的涌现行为标题： Quantifying Emergent Behaviors in Agent-Based Models using Mean Information Gain评论： 5页，4图主题： 物理与社会 (physics.soc-ph) ; 适应性与自组织系统 (nlin.AO)
涌现行为是复杂系统的一个显著特征，但其定量表征仍然是一个开放性挑战，因为传统分类主要依赖于对时空模式的视觉检查。 在本信中，我们提出使用平均信息增益（MIG）作为度量标准，以量化基于代理的模型中的涌现现象。 MIG 是一种基于条件熵的度量标准，用于量化在已知某些属性的情况下，对结构中其他元素的信息缺乏程度。 我们将它应用于一个多智能体偏置随机游走模型，该模型再现了Wolfram的四种行为类别，并表明MIG能够区分这些行为。 这种度量标准将涌现行为的分析与经典的秩序、无序和熵的概念重新联系起来，从而实现了对收敛、周期、复杂和混沌状态的定量分类。 这种方法克服了在系统边界附近定性观察的模糊性，尤其是在大规模系统中，并提供了一个紧凑且可扩展的框架，用于识别和比较复杂系统中的涌现行为。
Emergent behaviors are a defining feature of complex systems, yet their quantitative characterization remains an open challenge, as traditional classifications rely mainly on visual inspection of spatio-temporal patterns. In this Letter, we propose using the Mean Information Gain (MIG) as a metric to quantify emergence in Agent-Based Models. The MIG is a conditional entropy-based metric that quantifies the lack of information about other elements in a structure given certain known properties. We apply it to a multi-agent biased random walk that reproduces Wolfram's four behavioral classes and show that MIG differentiates these behaviors. This metric reconnects the analysis of emergent behaviors with the classical notions of order, disorder, and entropy, thereby enabling the quantitative classification of regimes as convergent, periodic, complex, and chaotic. This approach overcomes the ambiguity of qualitative inspection near regime boundaries, particularly in large systems, and provides a compact, extensible framework for identifying and comparing emergent behaviors in complex systems.