Dynamic Behavior of Perturbed Logistic Model

Abstract

A model that represents the rate of changes of the population with limited environmental resources can be described by,

$$\frac{dp}{dt}=p(a–bp)+g(t,p)=p(t_0)=p_0$$

where $a$ measures the growth rate in the absence of the restriction force $b$ and $\frac{a}{b}$ is called the carrying capacity of the environment. The random perturbation $g(t,P)$ is generated by random change in the environment. The behavior of the solution of this model for continuous and discrete case when $g(t,P)=w(t)$ is density independent with a constant random factor $w$ in a short time interval $[t,t+\delta t)$ will be studied. The stability and the behavior of the equilibrium point will also be investigated. A computational approach to the solution using Excel spreadsheet and Maple will be presented.