Stability and Local Hopf Bifurcation for a Predator-Prey Model with Delay

Abstract EN

A predator-prey system with disease in the predator is investigated, where the discrete delay τ is regarded as a parameter.

Its dynamics are studied in terms of local analysis and Hopf bifurcation analysis.

By analyzing the associated characteristic equation, it is found that Hopf bifurcation occurs when τ crosses some critical values.

Using the normal form theory and center manifold argument, the explicit formulae which determine the stability, direction, and other properties of bifurcating periodic solutions are derived.