Related papers: Flocking and concentration behavior for the stocha…
We study equilibrium selection for invariant measures of stochastic dynamical systems with constant step size, under persistent noise and minimal moment assumptions, in a general quasi-Feller framework. Such dynamics arise in…
Field theory tools are applied to analytically study fluctuation and correlation effects in spatially extended stochastic predator-prey systems. In the mean-field rate equation approximation, the classic Lotka-Volterra model is…
The functional method to derive the fractional Fokker-Planck equation for probability distribution from the Langevin equation with Levy stable noise is proposed. For the Cauchy stable noise we obtain the exact stationary probability density…
The collective motion of self-driven agents is a phenomenon of great interest in interacting particle systems. In this paper, we develop and analyze a model of agent motion in one dimension with periodic boundaries using a stochastic…
We employ the circular cumulant approach to construct a low dimensional description of the macroscopic dynamics of populations of phase oscillators (elements) subject to non-Gaussian white noise. Two-cumulant reduction equations for…
Patterns in complex systems store hidden information of the system which is needed to be explored. We present a simple model of cytokine and T-cells interaction and studied the model within stochastic framework by constructing Master…
The creation and subsequent evolution of marginally-unstable modes have been observed in a wide range of fusion devices. This behaviour has been successfully explained, for a single frequency shifting mode, in terms of phase-space…
We investigate the large population dynamics of a family of stochastic particle systems with three-state cyclic individual behaviour and parameter-dependent transition rates. On short time scales, the dynamics turns out to be approximated…
Natural flocks (aligned) and swarms (non-aligned) both exhibit features of near-criticality, challenging their treatment as two ends of the same phase transition. We present a model for the aggregation of active individuals, in which their…
We present a simple proof of asymptotic consensus in the discrete Hegselmann-Krause model and flocking in the discrete Cucker-Smale model with renormalization and variable delay. It is based on convexity of the renormalized communication…
We study clustering in a stochastic system of particles sliding down a fluctuating surface in one and two dimensions. In steady state, the density-density correlation function is a scaling function of separation and system size.This scaling…
We study the collective dynamics of a lattice model of stochastically interacting agents with a weighted field of vision. We assume that agents preferentially interact with neighbours, depending on their relative location, through velocity…
We introduce a family of lattice-gas models of flocking, whose thermodynamically consistent dynamics admits a proper equilibrium limit at vanishing self-propulsion. These models are amenable to an exact coarse-graining which allows us to…
In this paper, we study the behavior of systems of individuals in confined environments that are driven by laws of self-organization. We propose that, under certain conditions, the long-term behavior of such systems will be global…
Gaussian white noise is frequently used to model fluctuations in physical systems. In Fokker-Planck theory, this leads to a vanishing probability density near the absorbing boundary of threshold models. Here we derive the boundary condition…
We consider a particle evolving in the quadratic potential and subject to a time-inhomogeneous frictional force and to a random force. The couple of its velocity and position is solution to a stochastic differential equation driven by an…
In this paper, we investigate the convergence in probability of a stochastic symplectic scheme for stochastic nonlinear Schr\"{o}dinger equation with quadratic potential and an additive noise. Theoretical analysis shows that our symplectic…
Noise induced changes in the critical and oscillatory behavior of a Prey-Predator system are studied using power spectrum density and Spectral Amplification Factor (SAF) analysis. In the absence of external noise, the population densities…
In this paper, a delay Vlasov-Fokker-Planck equation associated to a stochastic interacting particle system with delay is investigated analytically. Under certain restrictions on the parameters well-posedness and ergodicity of the…
In this chapter, we present the Cucker-Smale type flocking models, and discuss their mathematical structures and flocking theorems in terms of coupling strength, interaction topologies and initial data. In 2007, two mathematicians Felipe…