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Seasonally perturbed prey-predator ecological system with the Beddington-DeAngelis functional response. (English) Zbl 1233.92081
Summary: On the basis of the theories and methods of ecology and ordinary differential equations, a seasonally perturbed prey-predator system with Beddington-DeAngelis functional response is studied analytically and numerically. Mathematical theoretical works have been pursuing the investigation of uniformly persistence, which depicts the threshold expression of some critical parameters. Numerical analyses indicate that seasonality has a strong effect on the dynamical complexity and species biomass using bifurcation diagrams and Poincaré sections. The results show that the seasonality in three different parameters can give rise to rich and complex dynamical behaviors. In addition, the largest Lyapunov exponents are computed. These computations further confirm the existence of chaotic behavior and the accuracy of the numerical simulations. All these results are expected to be of use in the study of the dynamic complexity of ecosystems.
MSC:
92D40Ecology
34C60Qualitative investigation and simulation of models (ODE)
37N25Dynamical systems in biology
65C20Models (numerical methods)
93A30Mathematical modelling of systems