Dynamics of an Impulsive Stochastic Nonautonomous Chemostat Model with Two Different Growth Rates in a Polluted Environment

Abstract

This paper proposes a novel impulsive stochastic nonautonomous chemostat model with the saturated and bilinear growth rates in a polluted environment. Using the theory of impulsive differential equations and Lyapunov functions method, we first investigate the dynamics of the stochastic system and establish the sufficient conditions for the extinction and the permanence of the microorganisms. Then we demonstrate that the stochastic periodic system has at least one nontrivial positive periodic solution. The results show that both impulsive toxicant input and stochastic noise have great effects on the survival and extinction of the microorganisms. Furthermore, a series of numerical simulations are presented to illustrate the performance of the theoretical results.

Threshold Analysis and Stationary Distribution of a Stochastic Model with Relapse and Temporary Immunity

“…In order to make this model more reasonable, we can also investigate delay stochastic differential equation models, control stochastic differential equation models, and impulsive stochastic differential equation models of system (2) for further work. The approaches are shown in [27][28][29][30][31][32][33][34][35][36][37][38][39][40][41].…”

Stationary Distribution and Periodic Solution of Stochastic Toxin-Producing Phytoplankton–Zooplankton Systems

“…Indeed, stochastic models could be more appropriate way of modeling in comparison with their deterministic counterparts, since they can provide some additional degree of realism. By introducing (stochastic) environmental noise, many investigators have studied stochastic epidemic models [14][15][16][17][18][19][20][21][22][23] and stochastic population models [24][25][26][27][28][29][30][31][32][33][34][35][36][37][38][39][40][41][42]. ey focus on the e ect of environmental uctuations on the dynamic behavior of these models.…”

Dynamics and Optimal Harvesting Control for a Stochastic One‐Predator‐Two‐Prey Time Delay System with Jumps

“…Therefore, many researchers have studied the Lotka-Volterra time delay models with two competitive preys and one predator [22,23]. Notice that the composite population systems with stochastic effects and time delays present some complex dynamics; thus this causes widespread researchers concern [24][25][26][27][28][29][30].…”