Related papers: Comment on ``Phase Transitions in Systems of Self-…
Understanding information transfer among individuals is fundamental to revealing collective dynamics of complex systems. Information transfers are quantified by information-theoretical measures and are often correlated with the concept of…
We consider the Czir\'ok model for collective motion of locusts along a one-dimensional torus. In the model, each agent's velocity locally interacts with other agents' velocities in the system, and there is also exogenous randomness to each…
We study the short-time dynamics (STD) of the Vicsek model with vector noise. The study of STD has proved to be very useful in the determination of the critical point, critical exponents, and spinodal points in equilibrium phase…
A recent paper [F. Radicchi and A. Arenas, Nature Phys. 9, 717 (2013)] presented the finding of an abrupt transition in the structure of interconnected networks. This transition was said to be generic and to occur even in networks of finite…
The Vicsek model of flocking is studied by computer simulation. We confined our studies here to the morphologies and the lifetimes of transient phases. In our simulation, we have identified three distinct transient phases, namely, vortex…
We consider the discrete Couzin-Vicsek algorithm (CVA), which describes the interactions of individuals among animal societies such as fish schools. In this article, we propose a kinetic (mean-field) version of the CVA model and provide its…
Effect of internal chirality on collective motion of a large number of active objects is studied by simulations of appropriately modified Vicsek model. We add a fixed angle to the noise and consider small ratios, $p$, between this angle and…
We have carried out a Monte Carlo simulation of a modified version of Vicsek model for the motion of self-propelled particles in two dimensions. In this model the neighborhood of interaction of a particle is a sector of the circle with the…
We study through numerical simulation the Vicsek model for very low speeds and densities. We consider scalar noise in 2-d and 3-d, and vector noise in 3-d. We focus on the behavior of the critical noise with density and speed, trying to…
Social relationships characterize the interactions that occur within social species and may have an important impact on collective animal motion. Here, we consider a variation of the standard Vicsek model for collective motion in which…
The dynamics of an ensemble of bistable elements under the influence of noise and with global time-delayed coupling is studied numerically by using a Langevin description and analytically by using 1) a Gaussian approximation and 2) a…
Diverse complex dynamical systems are known to exhibit abrupt regime shifts at bifurcation points of the saddle-node type. The dynamics of most of these systems, however, have a stochastic component resulting in noise driven regime shifts…
Attractors of dynamical systems may be networks in phase space that can be heteroclinic (where there are dynamical connections between simple invariant sets) or excitable (where a perturbation threshold needs to be crossed to a dynamical…
Collective dynamics result from interactions among noisy dynamical components. Examples include heartbeats, circadian rhythms, and various pattern formations. Because of noise in each component, collective dynamics inevitably involve…
The Vicsek model of self-propelled particles is known in three different phases: (i) a polar ordered homogeneous phase also called Toner-Tu phase, (iii) a phase of polar ordered regularly arranged high density bands (waves) with surrounding…
Recently, an Enskog-type kinetic theory for Vicsek-type models for self-propelled particles has been proposed [T. Ihle, Phys. Rev. E 83, 030901 (2011)]. This theory is based on an exact equation for a Markov chain in phase space and is not…
We study a control system resembling a singularly perturbed system whose variables are decomposed into groups that change their values with rates of different orders of magnitude. We establish that the slow trajectories of this system are…
In this paper we study phase transitions for weakly interacting multiagent systems. By investigating the linear response of a system composed of a finite number of agents, we are able to probe the emergence in the thermodynamic limit of a…
Weak multiplex percolation generalizes percolation to multi-layer networks, represented as networks with a common set of nodes linked by multiple types (colors) of edges. We report a novel discontinuous phase transition in this problem.…
In this paper, we study the phase transition behavior emerging from the interactions among multiple agents in the presence of noise. We propose a simple discrete-time model in which a group of non-mobile agents form either a fixed connected…