Complex dynamics in a prey predator system with multiple delays

The complex dynamics is explored in a prey predator system with multiple delays. Holling type-II functional response is assumed for prey dynamics. The predator dynamics is governed by modified Leslie–Gower scheme. The existence of periodic solutions via Hopf-bifurcation with respect to both delays are established. An algorithm is developed for drawing two-parametric bifurcation diagram with respect to two delays. The domain of stability with respect to τ1 and τ2 is thus obtained. The complex dynamical behavior of the system outside the domain of stability is evident from the exhaustive numerical simulation. Direction and stability of periodic solutions are also determined using normal form theory and center manifold argument.

► We model a prey predator with model with two discrete delays.
► Hopf-bifurcation analysis with respect to both delay parameters is performed.
► An algorithm has been developed to draw bifurcation diagram to obtain stability domain with respect to both delays.
► Complex dynamical behavior including chaos is obtained outside the domain of stability.
► Properties of periodic solutions are also determined.