On systems of active particles perturbed by symmetric bounded noises : a multiscale kinetic approach
Flora, Bruno Felice Filippo and Ciancio, Armando and d’Onofrio, Alberto (2021) On systems of active particles perturbed by symmetric bounded noises : a multiscale kinetic approach. Symmetry, 13 (9). 1604. ISSN 20738994 (https://doi.org/10.3390/sym13091604)
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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 HypoElliptical Fokker–Plank Equation (HEFPE). In presence of nonlocal BDIA, the resulting family of models is thus a Partial Integrodifferential Equation with hypoelliptical 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 noiseinduced 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.


Item type: Article ID code: 78068 Dates: DateEvent1 September 2021Published20 August 2021AcceptedKeywords: bounded noises, kinetic theory, active particles, statistical mechanics, population dynamics, Fokker–Planck equation, mathematical oncology, ecology, noise induced transitions, Mathematics, Physics, Chemistry, Mathematics(all), Computer Science (miscellaneous), Physics and Astronomy (miscellaneous), Chemistry (miscellaneous) Subjects: Science > Mathematics
Science > Physics
Science > ChemistryDepartment: Faculty of Science > Mathematics and Statistics Depositing user: Pure Administrator Date deposited: 07 Oct 2021 13:08 Last modified: 25 May 2023 11:02 URI: https://strathprints.strath.ac.uk/id/eprint/78068