Dynamic Behavior in a Delayed Bioeconomic Model with Stochastic Fluctuations

Abstract

The dynamic behavior of a bioeconomic model with time delay is investigated within stochastically fluctuating environment. Local stability and Hopf bifurcation condition are described on the delayed model system within deterministic environment. It reveals the sensitivity of the bioeconomic model dynamics on time delay. A phenomenon of Hopf bifurcation occurs as the time delay increases through a certain threshold. Subsequently, a stochastic model is discussed, which is established by incorporating white noise terms to the above deterministic delayed model system. With the help of numerical simulation, it can be shown that the frequency and amplitude of oscillation for the population density is enhanced as environmental driving forces increase.