Stability and Bifurcation of a Delayed Singular Prey-Predator Economic Model

Abstract

This paper studies a delayed singular prey-predator economic model, which is described by differential-algebraic equations due to a economic theory. Local stability and Hopf bifurcation condition are described on the delayed singular prey-predator economic model. It reveals the sensitivity of the 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.