Study on autonomous and nonautonomous version of a food chain model with intraspecific competition in top predator. (English) Zbl 1452.92045
Summary: In this article, a three-species food chain model with intraspecific competition in top predators has been considered. Ecological and mathematical well posedness of the model system has been established by showing that all the solutions of the model are positive and bounded. The extinction scenarios of intermediate and top predator species along with the existence and stability of all equilibrium points have been discussed. The effects of competition and conversion efficiency of top predators in the dynamics of the system have been discussed with great thrust, and it is observed that the conversion efficiency of top predators deteriorates the stability of the system, whereas intraspecific competition in top predators enhances the stable coexistence of all the populations of the system. Further, nonautonomous version of the model system has been taken into consideration to study the impact of seasonal variation in the dynamics of the model system. Sufficient conditions for the existence of a globally attractive positive periodic have been established in a periodic environment. Finally, numerical simulations have been carried out to validate our analytical findings.
MSC:
| 92D40 | Ecology |
| 34C11 | Growth and boundedness of solutions to ordinary differential equations |
| 34C23 | Bifurcation theory for ordinary differential equations |
| 34C25 | Periodic solutions to ordinary differential equations |
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