Lattice-gas model for collective biological motion

Csahók, Zoltán; Vicsek, Tamás

doi:10.1103/physreve.52.5297

Cited by 56 publications

(57 citation statements)

References 18 publications

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“…The above results caused a well-deserved stir and prompted a large number of studies at various levels [3,4,6,7,8,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37]. In particular, two of us showed that the onset of collective motion is in fact discontinuous [38], and that the original conclusion of Vicsek et al was based on numerical results obtained at too small sizes [5,9].…”

Section: Introductionmentioning

confidence: 97%

Collective motion of self-propelled particles interacting without cohesion

et al. 2008

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We present a comprehensive study of Vicsek-style self-propelled particle models in two and three space dimensions. The onset of collective motion in such stochastic models with only local alignment interactions is studied in detail and shown to be discontinuous (first-order like). The properties of the ordered, collectively moving phase are investigated. In a large domain of parameter space including the transition region, well-defined high-density and high-order propagating solitary structures are shown to dominate the dynamics. Far enough from the transition region, on the other hand, these objects are not present. A statistically-homogeneous ordered phase is then observed, which is characterized by anomalously-strong density fluctuations, superdiffusion, and strong intermittency.

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Section: Introductionmentioning

confidence: 97%

Collective motion of self-propelled particles interacting without cohesion

et al. 2008

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“…The only rule is that, at each time step, every particle approximates, with some uncertainty, the average direction of motion of the particles within its neighborhood of radius R. This model exhibits spontaneous self-organization; by decreasing the noise parameter, the system undergoes a kinetic phase transition from a disordered state to an ordered one where all the particles move approximately in the same direction. Due its simplicity and analogy with biological systems comprised of many, locally interacting particles, the SPP model soon became a reference model for the flocking behavior of organisms [13,14,15,16,17,18,19,20,21,22,23].…”

Section: Inroductionmentioning

confidence: 99%

Transitions in a self-propelled-particles model with coupling of accelerations

2009

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We consider a three dimensional, generalized version of the original SPP model for collective motion. By extending the factors influencing the ordering, we investigate the case when the movement of the self-propelled particles (SPP-s) depends on both the velocity and the acceleration of the neighboring particles, instead of being determined solely by the former one. By changing the value of a weight parameter s determining the relative influence of the velocity and the acceleration terms, the system undergoes a kinetic phase transition as a function of a behavioral pattern. Below a critical value of s the system exhibits disordered motion, while above it the dynamics resembles that of the SPP model. We argue that in nature evolutionary processes can drive the strategy variable s towards the critical point, where information exchange between the units of a system is maximal. InroductionCollective motion of organisms (e.g. fish schools, bird flocks, bacterial colonies) exhibits a large variety of emergent phenomena [1,2,3,4,5,6,7,8]. Synchronized motion, symmetrical group formations (e.g., V shaped) or swirling patterns emerge in spite of the apparently simple behavioral rules of the individual flock members [9,10]. The self propelled particles (SPP) model was proposed by Vicsek et al.[11] to describe the onset of ordered motion within a group of self-propelled particles in the presence of perturbations. Taking into the effects of fluctuations inevitably present in biological systems was an essential generalization of the prior deterministic flocking models such as that of Reynolds [12]. The original model considers point-like particles moving at constant velocity on a two dimensional surface with periodic boundary conditions. The only rule is that, at each time step, every particle approximates, with some uncertainty, the average direction of motion of the particles within its neighborhood of radius R. This model exhibits spontaneous self-organization; by decreasing the noise parameter, the system undergoes a kinetic phase transition from a disordered state to an ordered one where all the particles move approximately in the same direction. Due its simplicity and analogy with biological systems comprised of many, locally interacting particles, the SPP model soon became a reference model for the flocking behavior of organisms [13,14,15,16,17,18,19,20,21,22,23].The individual based behavioral rules, determining collective motion, are of particular interest. Important elements of behavioral rules are the nature of the perceived information and the affected behavioral traits. [24,25,26]. A frequent assumption in models is that the information, perceived by the particles, is restricted to the velocity of their neighbors. The interaction range is usually defined by metric distances, but Ballerini et al. [24] recently showed that topological distance is the one determining the flocking of starlings. The assumption of reflecting on the momentary velocity only may not be enough for adequately describing a number o...

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“…The external state of each individual has q states as in Potts model which is corresponding to q moving directions. The external state is similar to the definition of the individuals in the lattice gas model developed by Csahók et al [18]. But in our model, the rules of interaction between the two individuals are controlled by their internal state, i.e., there is no interaction if and only if both individuals are in non-excited state.…”

Section: Discussionmentioning

confidence: 86%

Monte-Carlo Study of the Collective Behavior in Animal Group: A \(q\)-state Potts model

Ngo¹

2015

Comm. in Phys.

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Abstract. We study in this work the phase transition behaviour of animal groups. We assume that the individuals in the group have two classes of state. One is the internal state which can be either excited or non-excited. The other one is characterized by their orientation or direction of motion, it is so called the external state. The internal state plays an important role in the rules of interaction between the individuals. The system is put under a source of external perturbation called "noise", the individuals can freely move from one site to another site on a two-dimension triangular lattice. We use the Monte-Carlo simulation technique for studying the behavior of the model with varying noise. For simplicity, we consider the orientation of individuals which has q states as in the Potts model. We show that the system has three phases which correspond to the uncollected, flocking and runaway behaviors at very low, medium and high noise, respectively. These phases are separated by two first-order transitions.

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Lattice-gas model for collective biological motion

Abstract: A simple self-driven lattice-gas model for collective biological motion is introduced. We find weakly first order phase transition from individual random walks to collective migration. A meanfield theory is presented to support the numerical results.

Cited by 56 publications

References 18 publications

Collective motion of self-propelled particles interacting without cohesion

Collective motion of self-propelled particles interacting without cohesion

Transitions in a self-propelled-particles model with coupling of accelerations

Monte-Carlo Study of the Collective Behavior in Animal Group: A \(q\)-state Potts model

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