标题： 超混沌和在$N$维神经元格子中的复杂动力学区域 显示英文标题

标题： Hyperchaos and complex dynamical regimes in $N$-dimensional neuron lattices

摘要： 我们研究了非混沌Rulkov神经元的$N$维晶格在电流流动耦合下的动力学特性。 我们考虑了最近邻和次近邻耦合、同质和异质神经元，以及在广泛电流耦合强度下的小和大晶格。 当耦合强度变化时，神经元表现出多种复杂的动态模式，包括不同步的混沌放电、局部准爆发、同步的混沌爆发和同步的超混沌。 对于更高空间维度的晶格，我们发现了由于许多连接神经元的“破坏性干涉”产生的动力学效应，以及由协调放电阈值交叉引起的微小“相变”。 在大型二维和三维神经元晶格中，我们观察到了如局部同步、准同步和滞后同步等涌现动力学。 这些结果展示了多维空间中耦合神经元所涌现的丰富动力学，突显了维度、连通性和异质性如何关键地塑造神经系统的集体行为。 显示英文摘要

摘要： We study the dynamics of $N$-dimensional lattices of nonchaotic Rulkov neurons coupled with a flow of electrical current. We consider both nearest-neighbor and next-nearest-neighbor couplings, homogeneous and heterogeneous neurons, and small and large lattices over a wide range of electrical coupling strengths. As the coupling strength is varied, the neurons exhibit a number of complex dynamical regimes, including unsynchronized chaotic spiking, local quasi-bursting, synchronized chaotic bursting, and synchronized hyperchaos. For lattices in higher spatial dimensions, we discover dynamical effects arising from the "destructive interference" of many connected neurons and miniature "phase transitions" from coordinated spiking threshold crossings. In large two- and three-dimensional neuron lattices, we observe emergent dynamics such as local synchronization, quasi-synchronization, and lag synchronization. These results illustrate the rich dynamics that emerge from coupled neurons in multiple spatial dimensions, highlighting how dimensionality, connectivity, and heterogeneity critically shape the collective behavior of neuronal systems.