Stage Structured Prey Predator Model with Maturation and Gestation Delay for Predator using Holling Type 2 Functional Response

Abstract

In this paper, we have proposed a prey predator model with stage structuring in predator. We have incorporated maturation and gestation delay in predator class. The positivity, boundedness, existence of equilibrium points and local stability has been discussed. We have also obtained threshold for maturation and gestation delay. If 0 < т₁ < т^*₁ then E* is locally asymptotically stable and when т₁ >т^*₁ , Hopf bifurcation exist in the absence of т .
Further, for т ≥ 0, E* is locally asymptotically stable if 0 < т < т* and for т > т*, it looss its stability. Finally, permanence of the system is discussed with numerical example in validation to the analytical results using MATLAB software.

Key words and phrases. Stage structure, Gestation delay, maturation delay,Local stability, Hopf bifurcation, Permanence.

2000 Mathematics Subject Classification. 34A37, 92D25