On competitive Lotka–Volterra model in random environments

Abstract

Keywords:Lotka-Volterra model Random environment Regime-switching diffusion Asymptotic property Long-run-average limit Focusing on competitive Lotka-Volterra model in random environments, this paper uses regime-switching diffusions to model the dynamics of the population sizes of n different species in an ecosystem subject to the random changes of the external environment. It is demonstrated that the growth rates of the population sizes of the species are bounded above. Moreover, certain long-run-average limits of the solution are examined from several angles. A partial stochastic principle of competitive exclusion is also derived. Finally, simple examples are used to demonstrate our findings.

On a non-autonomous stochastic Lotka-Volterra competitive system

“…One could study more realistic but more complex models, for example, stochastic systems under regime switching (see e.g., [30,40]), or with Lévy jumps (see e.g., [29]), or with reaction-diffusion ( [5]). Also it is interesting to study n-dimensional stochastic food chain model or cooperative system, and we leave these for future work.…”

Population dynamical behaviors of stochastic logistic system with jumps

“…Proof Our proof is motivated by Zhu and Yin [26]. Applying Itô's formula to [e t ln x(t)] leads to (1 + c(s, z)) N (ds, dz), and then…”

Persistence in mean and extinction on stochastic competitive Gilpin-Ayala systems with regime switching

“…However, the approaches proposed by these authors (see e.g. [12][13][14], and [15]) for Lotka-Volterra systems cannot be easily used in stochastic Gilpin-Ayala systems because of the nonlinear item. Meanwhile, the methods proposed in [16] and [17] cannot be readily applied to the asymptotic analysis owing to the existence of regime-switching mechanism, which can make the problem insolvable.…”