Dynamics of a single predator multiple prey model with stochastic perturbation and seasonal variation

Abstract

Considering various factors are stochastic rather than deterministic in the evolution of populations growth, in this paper, we propose a single predator multiple prey stochastic model with seasonal variation. By using the method of solving an explicit solution, the existence of global positive solution of this model are obtained. The method is more convenient than Lyapunov analysis method for some population models. Moreover, the stochastically ultimate boundedness are considered by using the comparison theorem of stochastic differential equation. Further, some sufficient conditions for the extinction and strong persistence in the mean of populations are discussed, respectively. In addition, by constructing some suitable Lyapunov functions, we show that this model admits at least one periodic solution. Finally, numerical simulations clearly illustrate the main theoretical results and the effects of white noise and seasonal variation for the persistence and extinction of populations.

A pseudo‐operational collocation method for variable‐order time‐space fractional KdV–Burgers–Kuramoto equation

“…Interest in fractional partial differential equations (FPDEs) and fractional ordinary differential equations (FODEs) is due to their diverse applications in different domains of science and engineering such as unstable drift waves in plasma, 1 solute transport in groundwater, 2 dynamic of viscoelastic materials, 3,4 continuum and statistical mechanics, 5 colored noise, 6 signal processing, 7 kinetic theory of gasses, 8 cyber‐physical system, 9 biology, 10–12 and so on. Different deffinitions of fractional integral and derivative operators have appeared in various categories of FPDEs and FODEs, such as the Riemann–Liouville, Caputo, Grünwald–Letnikov, Ortigueira–Caputo, and Atangana–Baleanu–Caputo fractional integrals and derivatives 3,13–16 .…”