Dynamics of a delayed predator-prey system with stage structure and cooperation for preys

In this paper we have taken a delayed predator-prey system with stage structure among prey species. We assume that there is cooperation among the mature and immature preys to ensure immature prey's existence and there is a maturation delay for immature to be mature for the preys. With this model the local stability has been discussed in presence of delay. By taking maturation delay as the key parameter, the condition for local stability has been obtained by constructing a Lyapunov functional. By taking the maturation delay as the bifurcation parameter the necessary conditions for Hopf-bifurcation have been discussed both analytically and numerically. The length of delay has been estimated to preserve the stability. Also, Lyapunov exponents have been evaluated numerically for different cases.