Dynamical behaviors of a stochastic delay logistic system with impulsive toxicant input in a polluted environment.

A stochastic delay logistic system with Markov switching and impulsive toxicant input in a polluted environment is proposed and studied. Some sufficient criteria for extinction, non-persistence in the mean and weak persistence of the solutions are established.

[1]  Zhenqing Li,et al.  Dynamic analysis of Michaelis–Menten chemostat-type competition models with time delay and pulse in a polluted environment , 2009 .

[2]  Thomas G. Hallam,et al.  Effects of toxicants on populations: a qualitative approach I. Equilibrium environmental exposure , 1983 .

[3]  Jianjun Jiao,et al.  Dynamical analysis of a five-dimensioned chemostat model with impulsive diffusion and pulse input environmental toxicant , 2011 .

[4]  T. Gard Stochastic models for toxicant-stressed populations. , 1992, Bulletin of mathematical biology.

[5]  Bing Liu,et al.  The Effects of Impulsive Toxicant Input on a Population in a Polluted Environment , 2003 .

[6]  Thomas G. Hallam,et al.  Effects of toxicants on populations: A qualitative: Approach III. Environmental and food chain pathways* , 1984 .

[7]  Lei Zhang,et al.  Dynamics of a two-species Lotka-Volterra competition system in a polluted environment with pulse toxicant input , 2009, Appl. Math. Comput..

[8]  Ke Wang,et al.  Persistence and extinction of a single-species population system in a polluted environment with random perturbations and impulsive toxicant input , 2012 .

[9]  Jianjun Jiao,et al.  Dynamical analysis of a chemostat model with delayed response in growth and pulse input in polluted environment , 2009 .

[10]  Xuerong Mao,et al.  Stochastic Differential Equations With Markovian Switching , 2006 .

[11]  M. Liu,et al.  Persistence and extinction of a stochastic single-specie model under regime switching in a polluted environment. , 2010, Journal of theoretical biology.

[12]  X. Mao,et al.  Environmental Brownian noise suppresses explosions in population dynamics , 2002 .

[13]  Fengmei Tao,et al.  Dynamic Behaviors of a Single-Species Population Model With Birth Pulses in a Polluted Environment , 2008 .

[14]  Zhen Jin,et al.  Weak average persistence and extinction of a predator–prey system in a polluted environment with impulsive toxicant input☆ , 2007 .

[15]  T. Hallam,et al.  Effects of toxicants on populations: A qualitative approach II. first order kinetics , 1983, Journal of mathematical biology.

[16]  Xinyu Song,et al.  Extinction and permanence of chemostat model with pulsed input in a polluted environment , 2009 .

[17]  Jianjun Jiao,et al.  A single stage-structured population model with mature individuals in a polluted environment and pulse input of environmental toxin , 2009 .

[18]  T. Gard,et al.  Stability for multispecies population models in random environments , 1986 .

[19]  Wenxue Li,et al.  Persistence and extinction of a stochastic delay Logistic equation under regime switching , 2013, Appl. Math. Lett..

[20]  Ke Wang,et al.  Asymptotic properties and simulations of a stochastic logistic model under regime switching II , 2011, Math. Comput. Model..

[21]  Thomas C. Gard Persistence in stochastic food web models , 1984 .

[22]  Shaohong Cai,et al.  A stage-structured single species model with pulse input in a polluted environment , 2009 .