Title: Strange-attractor-driven matter Show Chinese title

Title: 由奇异吸引子驱动的物质

Abstract: Strange attractors can arise from nonlinear dynamical systems, however, such attractors may also be used to drive complex dynamics. We outline a flexible deterministic formalism for such chaos-driven dynamics. By using a strange attractor to model each particle's internal state space, we present a new class of matter coined ``strange-attractor-driven matter''. As an illustrative example, we show how the strange-attractor-driven matter can be used for modeling dynamics and collective behavior reminiscent of active matter. This leads to a flexible model that can be used to generate a variety of active particle motions, for example run-and-tumble and run-reverse-flick motions, as well as more exotic motions such as curlicued trajectories with continuously-changing direction induced by a Lorenz attractor. When combined with particle interactions, these strange-attractor-driven particles gives rise to several characteristic active-matter phenomena such as clustering, jamming and flocking. In addition, the presented model enables active control over the motion of emergent clusters, with complex flocking features such as fusion, splitting and collisions of flocks emerging spontaneously. Beyond the illustrative example of active matter, the formalism of strange-attractor-driven dynamics presented in this paper may be applicable more broadly, to model complex dynamical and emergent behaviors in a variety of contexts. Show Chinese abstract

Abstract: 奇异吸引子可以来自非线性动力系统，然而，这样的吸引子也可以用来驱动复杂动力学。 我们概述了一种灵活的确定性形式化方法用于这种混沌驱动的动力学。 通过使用奇异吸引子来模拟每个粒子的内部状态空间，我们提出了一类新的物质，称为“奇异吸引子驱动物质”。 作为一个示例，我们展示了奇异吸引子驱动物质如何用于建模类似于活性物质的动力学和集体行为。 这导致了一个灵活的模型，可用于生成多种活性粒子运动，例如跑-停和跑-反转-闪烁运动，以及由洛伦兹吸引子引起的连续改变方向的螺旋轨迹等更奇特的运动。 当与粒子相互作用结合时，这些奇异吸引子驱动粒子会引发几种典型的活性物质现象，如聚类、堵塞和 flocking（ flocking 为不可翻译内容，原样返回）。 此外，所提出的模型使得可以对涌现聚类的运动进行主动控制，复杂的 flocking 特征如 flock 的融合、分裂和碰撞会自发出现。 除了活性物质的示例之外，本文中提出的奇异吸引子驱动动力学的形式化方法可能更广泛适用，可用于在各种上下文中建模复杂动力学和涌现行为。