Dynamic Behavior of Perturbed Logistic Model

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

\[
\frac{dp}{dt} = p\left(a – {bp}\right) + g(t,p) = p(t_0)= p_0
\]

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.