Dynamic behavior of a Beddington–DeAngelis type stage structured predator–prey model

摘要

This paper deals with a robust stage structured predator–prey model with Beddington–DeAngelis-type functional response. The proposed mathematical model consists of a system of three nonlinear ordinary differential equations to stimulate the interactions between prey population, juvenile predators and adult predator population. The positivity, boundedness and the conditions for uniform persistence have been derived. The dynamical behavior of the system both analytically and numerically investigated from the point of view of local stability, persistence and global stability. The global stability of the system has been derived by using the theory of competitive systems, stability of periodic orbits and compound matrices for the interior equilibrium point. Depending on the conversion rate of the prey population to juvenile predator, the model exhibits Hopf-bifurcation. The model admit periodic solutions which is produced from the stage structure of the predator populations. Numerical simulations have been accomplished to validate our analytical findings.