Miranda-Filho L H, Sobral T A, de Souza A J F, Elskens Y, Romaguera Antonio R de C
Departamento de Física, Universidade Federal Rural de Pernambuco, Rua Manoel de Medeiros, s/n, Dois Irmãos, 52171-900, Recife, Brazil.
Instituto Federal de Educação, Ciência e Tecnologia do Rio Grande do Norte, RN 288, s/n, Nova Caicó, 59300-000, Caicó, Brazil.
Phys Rev E. 2022 Jan;105(1-1):014213. doi: 10.1103/PhysRevE.105.014213.
The well-known Vicsek model describes the dynamics of a flock of self-propelled particles (SPPs). Surprisingly, there is no direct measure of the chaotic behavior of such systems. Here we discuss the dynamical phase transition present in Vicsek systems in light of the largest Lyapunov exponent (LLE), which is numerically computed by following the dynamical evolution in tangent space for up to two million SPPs. As discontinuities in the neighbor weighting factor hinder the computations, we propose a smooth form of the Vicsek model. We find a chaotic regime for the collective behavior of the SPPs based on the LLE. The dependence of LLE with the applied noise, used as a control parameter, changes sensibly in the vicinity of the well-known transition points of the Vicsek model.
著名的维塞克模型描述了一群自驱动粒子（SPP）的动力学。令人惊讶的是，对于此类系统的混沌行为没有直接的度量。在此，我们根据最大李雅普诺夫指数（LLE）来讨论维塞克系统中存在的动力学相变，该指数是通过在切空间中跟踪多达两百万个SPP的动力学演化进行数值计算得到的。由于邻居加权因子中的不连续性阻碍了计算，我们提出了一种维塞克模型的平滑形式。基于LLE，我们发现了SPP集体行为的混沌区域。作为控制参数的LLE与所施加噪声的依赖关系在维塞克模型的著名转变点附近有明显变化。
