Stability and bifurcation of a prey–predator model with time delay

In this article a system of retarded differential equations is proposed as a predator–prey model. We investigate the model, representing a resource (prey) and a two predator system with delay due to gestation. The response function is assumed here to be concave in nature. Since global stability of positive equilibrium is of great interest, we provide sufficient conditions in terms of parameters of the system to guarantee it. By the simulation process the bifurcation occurring are discussed in terms of two bifurcation parameters. We have also shown that the time delay can cause a stable equilibrium to become unstable and even switching of stabilities. Numerical simulations are given to illustrate the results. To cite this article: T.K. Kar, A. Batabyal, C. R. Biologies 332 (2009).