V. Madhusudanan, S. Vijaya, Dynamical Behaviour in Two Prey-Predator System with Persistence, BMSA Volume 16, Bulletin of Mathematical Sciences and Applications (Volume 16)
https://www.scipress.com/BMSA.16.20
Abstract:
    In this work, the dynamical behavior of the system with two preys and one predator population is investigated. The predator exhibits a Holling type II response to one prey which is harvested and a Beddington-DeAngelis functional response to the other prey. The boundedness of the system is analyzed. We examine the occurrence of positive equilibrium points and stability of the system at those points. At trivial equilibrium E<sub>0</sub> and axial equilibrium (E<sub>1</sub>); the system is found to be unstable. Also we obtain the necessary and sufficient conditions for existence of interior equilibrium point (E<sub>6</sub>) and local and global stability of the system at the interior equilibrium (E<sub>6</sub>): Depending upon the existence of limit cycle, the persistence condition is established for the system. The numerical simulation infer that varying the parameters such as e and λ<sub>1</sub> it is possible to change the dynamical behavior of the system from limit cycle to stable spiral. It is also observed that the harvesting rate plays a crucial role in stabilizing the system.
Keywords:
    Functional Response, Global Stability, Harvesting, Local Stability, Persistence