Hopf bifurcation analysis for a harvested differential-algebraic prey-predator model

In this paper, by means of Hopf bifurcation theory and the normal form method, Hopf bifurcation and local stability for a differential-algebraic predator-prey model with predator harvesting are considered. Our model is described by differential-algebraic equations due to economic factors are introduced into a traditional Lotka-Volterra predator-prey system. It shows that periodic solution occurs when the bifurcation parameter exceeds a certain limit. Some algebraic criteria on these issues are derived. Lastly, some numerical simulations are provided to support the effectiveness of our findings.