On systems of active particles perturbed by symmetric bounded noises: a multiscale kinetic approach

Bruno Felice Filippo Flora, Armando Ciancio, Alberto d’Onofrio

Research output: Contribution to journalArticlepeer-review

Abstract

We consider an ensemble of active particles, i.e., of agents endowed by internal variables u(t). Namely, we assume that the nonlinear dynamics of u is perturbed by realistic bounded symmetric stochastic perturbations acting nonlinearly or linearly. In the absence of birth, death and interactions of the agents (BDIA) the system evolution is ruled by a multidimensional Hypo-Elliptical Fokker–Plank Equation (HEFPE). In presence of nonlocal BDIA, the resulting family of models is thus a Partial Integro-differential Equation with hypo-elliptical terms. In the numerical simulations we focus on a simple case where the unperturbed dynamics of the agents is of logistic type and the bounded perturbations are of the Doering–Cai–Lin noise or the Arctan bounded noise. We then find the evolution and the steady state of the HEFPE. The steady state density is, in some cases, multimodal due to noise-induced transitions. Then we assume the steady state density as the initial condition for the full system evolution. Namely we modeled the vital dynamics of the agents as logistic nonlocal, as it depends on the whole size of the population. Our simulations suggest that both the steady states density and the total population size strongly depends on the type of bounded noise. Phenomena as transitions to bimodality and to asymmetry also occur.
Original languageEnglish
Article number1604
Number of pages23
JournalSymmetry
Volume13
Issue number9
DOIs
Publication statusPublished - 1 Sep 2021

Keywords

  • bounded noises
  • kinetic theory
  • active particles
  • statistical mechanics
  • population dynamics
  • Fokker–Planck equation
  • mathematical oncology
  • ecology
  • noise induced transitions

Fingerprint

Dive into the research topics of 'On systems of active particles perturbed by symmetric bounded noises: a multiscale kinetic approach'. Together they form a unique fingerprint.

Cite this