Collective Motion in a System of Motile Elements

Abstract

Clusters of biological organisms often show diverse collective motions. Considering the physical properties of active elements with mutual interactions, we propose a mathematical model of collective motion. Several kinds of cluster motion seen in nature, including collective rotation, chaos, and wandering, occur in computer simulations of our deterministic model. By introducing a set of dimensionless parameters, we categorize the collective motions and obtain their phase diagram. We analyze the collective motions with a disorder parameter and Lyapunov spectra to characterize their transitions. [S0031-9007(96)00218-9]

Gaussian theory for spatially distributed self-propelled particles

“…The result of the model is surprising because it introduces a new class of transitions with continuous symmetry breaking in two dimensions [28,29]. Later, many different studies were done to capture other interesting behavior of active matter [27,[30][31][32][33][34][35][36][37][38][39][40][41][42].…”

Collective behavior of interacting self-propelled particles

“…As the motion of flocking organisms is usually controlled by interactions with their neighbors [1], the SPP models consist of locally interacting particles with an intrinsic driving force, hence with a finite steady velocity. Because of their simplicity, such models represent a statistical approach complementing other studies which take into account more details of the actual behavior [6,9,10], but treat only a moderate number of organisms and concentrate less on the large scale behavior.…”

Cohesive motion in one-dimensional flocking

“…The formulations to study the flocking phenomenon can be succinctly classified in rule-based [10,11,12,13,14,15,16,17,18], Lagrangian (trajectory-based) [19,20,21,22,23,24,25,26] and Eulerian (continuum) models [27,28,29]. Regarding the dimensionality of the models developed, most of them have been defined in dimensions higher than one [10,11,12,13,14,15,20,21,22,23,24,25,27,28,29,30], since the velocity of the self-propelled particles (SPP) in these models can have continuous values. In contrast, only a few one-dimensional (1D) models have been studied [5,16,17,18,19,26,31].…”