Stability Analysis of Food Chain System with Presence of Middle Predators Refuge and Mutual Interaction for The Top Predator with Reserved Zone
DOI:
https://doi.org/10.24237/04.04.883Keywords:
food chain stabilityAbstract
The aim of this work is to study local and global stability of a food chain dynamical system with wholly dependence top predator in a reserved zone, investigating mutualistic interaction of the top predator with both the prey and the middle predator as indemnity Holling type II functional response to obtain food in an ecologically reserved zone, where the prey and the middle predator coexist outgoing the reserved zone while the top predator easily burrows between them, the system boundedness demonstrated, the existence of the five feasible equilibrium points was proven. The sufficient conditions of local and global stability of equilibrium points shown briefly. Persistence of the food chain system studied with support of average Lyapunov function. A numerical simulation utilized to assure the theoretical outcomes. Finally, the research results concluded via a conclusion.
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