Dynamic Behavior Of Stochastic Biological Models Under The Influence Of White Noise

Many scholars have studied the dynamic behavior of biological models by es-tablishing deterministic models. However, any individual organisms of the nature is inevitably affected by its quantity change and random factor of external envi-ronment. Therefore, the stochastic model can reflect the actual more accurately. In this paper, we study the dynamic behavior of stochastic biological models under the influence of white noise. The content of this paper is as follows.1. Dynamic behavior of a stochastic eco-epidemiological model with Holling type II functional response. We consider the stochastic model with infectious trans-mission rate perturbed by white noise. The sufficient conditions for the stochas-tic stability, its long time behavior around the equilibrium of deterministic eco-epidemiological model and the stochastic asymptotic stability are presented by Lyapunov analysis methods.2. The principle of competitive exclusion about stochastic biological models. We consider a stochastic Lotka-Volterra model with two predators competing for one prey and a stochastic chemostat model with Holling type II functional response. The sufficient conditions which guarantee the principle of competitive exclusion for these perturbed models are given via using Lyapunov analysis methods.3. Periodic solution for stochastic non-autonomous Lotka-Volterra models in a polluted environment. We consider a stochastic non-autonomous competi-tive model, a stochastic non-autonomous mutualism model and a stochastic non-autonomous predator-prey model. The sufficient condition for the existence and global attractivity of a nontrivial positive periodic solution is given by the existence theorem of the periodic solution due to Hasminskii.