Collective dynamics of self-propelled particles with variable speed

Abstract

Understanding the organization of collective motion in biological systems is an ongoing challenge. In this paper we consider a minimal model of self-propelled particles with variable speed. Inspired by experimental data from schooling fish, we introduce a power-law dependency of the speed of each particle on the degree of polarization order in its neighborhood. We derive analytically a coarse-grained continuous approximation for this model and find that, while the specific variable speed rule used does not change the details of the ordering transition leading to collective motion, it induces an inverse power-law correlation between the speed or the local polarization order and the local density. Using numerical simulations, we verify the range of validity of this continuous description and explore regimes beyond it. We discover, in disordered states close to the transition, a phase-segregated regime where most particles cluster into almost static groups surrounded by isolated high-speed particles. We argue that the mechanism responsible for this regime could be present in a wide range of collective motion dynamics.

From behavioural analyses to models of collective motion in fish schools

“…This has been shown for instance by Gautrais et al [40], who detected a change in behavioural parameters with increasing density, leading to a disordered swimming once a critical density has been reached. It is worth noting that in that particular case, the individuals may change their behaviour relative to the density [91]. This additional coupling, namely the influence of the school as a whole on the behaviour of its constituent individuals, is a topic that we may carefully consider in future investigations.…”

“…the school) is highly polarized [60]. This critical change in global behaviour is obtained by varying the value of a behavioural parameter such as noise [60,90], blind angle size [65], speed [91], alignment tendency [62] or a 'strategy parameter' [92], which weighs a behavioural compromise between aligning with neighbours and reacting to their direction changes. The validity of this view finds some support in the experimental work of Becco et al [93] that showed that such transition from disorder to order can be obtained by increasing the density of Tilapia fish in a shallow water arena.…”

Promoting collective motion of self-propelled agents by distance-based influence

“…In recent years, a variety of efforts have been devoted to modeling the dynamic properties of swarms [15][16][17][18][19][20][21][22][23][24][25][26][27]. In 1995, Vicsek et al proposed a particularly simple but rich model [28].…”

Entropic Ratchet transport of interacting active Brownian particles

“…However, active matters in biological and physical systems have been studied theoretically and experimentally [12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28]. The kinetics of active particles moving in periodic structures could exhibit peculiar behaviors.…”