相关论文: Phase transition and asymptotic behaviour of flock…

The hydrodynamic limit of a kinetic Cucker-Smale model is investigated. In addition to the free-transport of individuals and the Cucker-Smale alignment operator, the model under consideration includes a strong local alignment term. This…

Consider a string of N+1 damped oscillators moving on the line of which the motion of the first (called the "leader") is independent of the others. Each of the followers `observes' the relative velocity and position of only its nearest…

A model of noise reduction (NR) for signal processing is introduced. Each noise source puts a symmetric constraint on the space of the signal vector within a tolerable overlap. When the number of noise sources increases, sequences of…

We study the convergence properties of the conditional (Kullback-Leibler) entropy in stochastic systems. We have proved very general results showing that asymptotic stability is a necessary and sufficient condition for the monotone…

We obtain equilibration rates for a one-dimensional nonlocal Fokker-Planck equation with time-dependent diffusion coefficient and drift, modeling the relaxation of a large swarm of robots, feeling each other in terms of their distance,…

In this paper we consider the global stability of solutions of a nonlinear stochastic differential equation. The differential equation is a perturbed version of a globally stable linear autonomous equation with unique zero equilibrium where…

We introduce a Vicsek-like flocking model with a minimal form of time-delayed orientational interactions, in which the delays occur on a time scale that is well-separated from other time scales in the model. We achieve this by implementing…

We demonstrate a novel phase transition from stable to unstable fluid behaviour for fluid-filled cosmological spacetimes undergoing decelerated expansion. This transition occurs when the fluid speed of sound $c_S$ exceeds a critical value…

We study two variants of the modified Watts threshold model with a noise (with nonconformity, in the terminology of social psychology) on a complete graph. Within the first version, a noise is introduced via so-called independence, whereas…

We study a new flocking model which has the versatility to capture the physically realistic qualitative behavior of the Motsch-Tadmor model, while also retaining the entropy law, which lends to a similar 1D global well-posedness analysis to…

Given a stochastic nonlinear system controlled over a possibly noisy communication channel, the paper studies the largest class of channels for which there exist coding and control policies so that the closed-loop system is stochastically…

This paper considers the state transition of the stochastic Morris-Lecar neuronal model driven by symmetric $\alpha$-stable L\'evy noise. The considered system is bistable: a stable fixed point (resting state) and a stable limit cycle…

We use the Fokker-Planck equation and its moment equations to study the collective behavior of interacting particles in unsteady one-dimensional flows. Particles interact according to a long-range attractive and a short-range repulsive…

We investigate a general class of models for swarming/self-collective behaviour in domains with boundaries. The model is expressed as a stochastic system of interacting particles subject to both reflecting boundary condition and common…

In this paper we consider interacting particle systems which are frequently used to model collective behavior in animal swarms and other applications. We study the stability of orientationally aligned formations called flock solutions, one…

We investigate the most probable phase portrait (MPPP) of a stochastic single-species model with the Allee effect using the non-local Fokker-Planck equation. This stochastic model is driven by non-Gaussian as well as Gaussian noise, and it…

The combined influence of oscillatory excitations and multiplicative stochastic perturbations of white noise type on isochronous systems in the plane is investigated. It is assumed that the intensity of perturbations decays with time and…

We present approximate analytical method of analysis of stationary states of nonlinear quantum systems with the noise. As an example we consider quantum nonlinear oscillator excited by fluctuating force and found parameter regions with more…

A defect density which quantifies the deviation from the spin ground state characterizes non-equilibrium dynamics during phase transitions. The widely recognized Kibble-Zurek scaling predicts how the defect density evolves during phase…

Animals having a trend to align their velocities to an average of their neighbors' may flock as illustrated by the Vicsek model and its variants. If, in addition, they feel a systematic contrarian trend, the result may be a time periodic…