标题： 追逐-逃避与非局部模式形成中的手性模型 显示英文标题

标题： Chase-and-Run and Chirality in Nonlocal Models of Pattern Formation

摘要： 追逐-逃逸动力学（其中一个群体追逐另一个群体且后者逃离前者）在自然界中随处可见，从生态系统中的捕食者-猎物相互作用到发育过程中细胞的集体运动。 有趣的是，在许多这些系统中，运动并不是直线；相反，“逃跑者”会以一个角度偏离其追逐者。 这种角度运动通常表现出一致的左右不对称性，被称为侧化或手性。 受斑马鱼皮肤模式和规避动物运动现象的启发，我们探索了手性如何塑造非局部（积分微分）对流-扩散模型中的模式形成。 我们将此类模型扩展以允许任意角度的移动，揭示出行为的丰富图景。 我们发现手性可以增强模式形成，抑制振荡，并产生全新的动态结构，例如旋转的追逐者和逃跑者的脉冲。 我们还揭示了追逐-逃逸动力学如何导致种群混合或分离。 通过线性稳定性分析，我们确定了一些驱动这些效应的物理机制，同时也暴露了该理论在捕捉更复杂动态时的显著局限性。 我们的研究结果表明，手性可能在生态和细胞模式形成中扮演角色，而不仅仅是打破左右对称性。 显示英文摘要

摘要： Chase-and-run dynamics, in which one population pursues another that flees from it, are found throughout nature, from predator-prey interactions in ecosystems to the collective motion of cells during development. Intriguingly, in many of these systems, the movement is not straight; instead, 'runners' veer off at an angle from their pursuers. This angled movement often exhibits a consistent left-right asymmetry, known as lateralisation or chirality. Inspired by such phenomena in zebrafish skin patterns and evasive animal motion, we explore how chirality shapes the emergence of patterns in nonlocal (integro-differential) advection-diffusion models. We extend such models to allow movement at arbitrary angles, uncovering a rich landscape of behaviours. We find that chirality can enhance pattern formation, suppress oscillations, and give rise to entirely new dynamical structures, such as rotating pulses of chasers and runners. We also uncover how chase-and-run dynamics can cause populations to mix or separate. Through linear stability analysis, we identify physical mechanisms that drive some of these effects, whilst also exposing striking limitations of this theory in capturing more complex dynamics. Our findings suggest that chirality could have roles in ecological and cellular patterning beyond simply breaking left-right symmetry.