Phase Transitions in Systems of Self-Propelled Agents and Related Network Models

Aldana, Maximino; Dossetti, V.; Huepe, Cristián; Kenkre, V. M.; Larralde, Hernán

doi:10.1103/physrevlett.98.095702

Cited by 213 publications

(251 citation statements)

References 14 publications

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“…Many studies have explored the nature of the above phase transition (whether it is first or second order), finding that two factors play an important role: (i) the precise way that the noise is introduced into the system; and (ii) the speed v 0 with which the agents move (Aldana et al, 2007(Aldana et al, , 2009Baglietto and Albano, 2009;Gregoire and Chate, 2004;Pimentel et al, 2008). The Vicsek model raises a fundamental control problem: Under what conditions can the multi-agent system display a particular collective behavior?…”

Section: Vicsek Model and The Alignment Problemmentioning

confidence: 99%

Control principles of complex systems

Liu¹,

Barabási²

2016

Rev. Mod. Phys.

533

349

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A reflection of our ultimate understanding of a complex system is our ability to control its behavior. Typically, control has multiple prerequisites: it requires an accurate map of the network that governs the interactions between the system's components, a quantitative description of the dynamical laws that govern the temporal behavior of each component, and an ability to influence the state and temporal behavior of a selected subset of the components. With deep roots in nonlinear dynamics and control theory, notions of control and controllability have taken a new life recently in the study of complex networks, inspiring several fundamental questions: What are the control principles of complex systems? How do networks organize themselves to balance control with functionality? To address these here we review recent advances on the controllability and the control of complex networks, exploring the intricate interplay between a system's structure, captured by its network topology, and the dynamical laws that govern the interactions between the components. We match the pertinent mathematical results with empirical findings and applications. We show that uncovering the control principles of complex systems can help us explore and ultimately understand the fundamental laws that govern their behavior.

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Section: Vicsek Model and The Alignment Problemmentioning

confidence: 99%

Control principles of complex systems

Liu¹,

Barabási²

2016

Rev. Mod. Phys.

533

349

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“…In the original SPP model [11] (here, following the notation of Huepe and Aldana, Ref [22], called as the Original Vicsek Algorithm (OVA)) the positions of the particles at t + ∆t are depending on two previous time-steps, t and t − ∆t. In the literature some authors have implemented the model in a slightly different way [20,28,29,30], where the order of the position and the velocity update are changed. Huepe and Aldana [22] refer to this as the Standard Vicsek Algorithm (SVA) and they report that the local density is different in the OVA and the SVA, while in both cases the average number of interacting neighbors is unreasonably high because of the lack of a repulsive effect.…”

Section: Resultsmentioning

confidence: 99%

Turning with the Others: Novel Transitions in an SPP Model with Coupling of Accelerations

Szabó

Nagy

Vicsek

2008

2008 Second IEEE International Conference on Self-Adaptive and Self-Organizing Systems

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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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“…and a corresponding one for sine instead of cosine, which combined with Equations (13) and (14) givė…”

Section: Part I 2 Original Equationsmentioning

confidence: 99%

Ordered, Disordered and Partially Synchronized Schools of Fish

Birnir

Einarsson

Bonilla

et al. 2017

International Journal of Nonlinear Sciences and Numerical Simulation

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We study how an ODE description of schools of fish [1] changes in the presence of a random acceleration. The model can be reduced to one ODE for the direction of the velocity of a generic fish and another one for its speed. These equations contain the mean speedv and a Kuramoto order parameter for the phases of the fish velocities, r. We show that their stationary solutions consist of an incoherent unstable solution with r =v = 0 and a globally stable solution with r = 1 and a constantv > 0. In the latter solution, all fishes move uniformly in the same direction withv and the direction of motion determined by the initial configuration of the school. In the second part, the directional headings of the particles are perturbed, in two distinct ways, and the speeds accelerated in order to obtain two distinct classes of non-stationary, complex solutions. We show that the system has similar behavior as the unperturbed one, and derive the resulting constant value of the average speed, verified numerically. Finally, we show that the system exhibits a similar bifurcation to that in [2], between phases of synchronization and disorder. In one case, the variance of the angular noise, which is Brownian, is varied, and in the other case, varying the turning rate causes a similar phase transition.

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Phase Transitions in Systems of Self-Propelled Agents and Related Network Models

Cited by 213 publications

References 14 publications

Control principles of complex systems

Control principles of complex systems

Turning with the Others: Novel Transitions in an SPP Model with Coupling of Accelerations

Ordered, Disordered and Partially Synchronized Schools of Fish

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