Dynamic Behavior in a Singular Delayed Bioeconomic Model

Abstract

The effect of gestation delay on a singular bioeconomic model is investigated, which is described by differential-algebraic equations due to a economic theory. Local stability and Hopf bifurcation condition are described on the singular bioeconomic model with time delay. It reveals the sensitivity of the bioeconomic model dynamics on gestation time delay. A phenomenon of Hopf bifurcation occurs as the gestation time delay increases through a certain threshold. Numerical simulations are carried out to substantiate these theory analysis.