Dynamics of Stage-Structured Predator–Prey Model with Beddington–DeAngelis Functional Response and Harvesting

In this paper, we investigate the stability of equilibrium in stage-structured and density-dependent predator–prey system with Beddington–DeAngelis functional response. First, by checking sign real part for eigenvalue, local origin boundary are studied. Second, explore positive τ=0 τ≠0 (time delay τ is time taken from immaturity to maturity predator), which shows that dependent on parameter τ. Third, qualitatively analyze global asymptotical equilibrium. Based theory periodic solutions, obtained when τ=0; constructing Lyapunov functions, conclude also globally asymptotically stable τ≠0. Finally, examples numerical simulations given illustrate results.