Asymptotic stability of one prey and two predators model with two functional responses
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We formulate a mathematical model to study the complex dynamical behavior of a three dimensional model consisting of one prey and two predators involving Beddington–DeAngelis and Crowley–Martin functional responses. The existence and stability conditions of the equilibrium points are analyzed. The global asymptotic stability of the interior equilibrium point, if exists, is proved by considering Lyapunov function. Several numerical simulations are performed to illustrate the theoretical analysis. The multiple states of stability are observed in one example whereas another example exhibits the global stability of interior equilibrium point.
KeywordsPrey–predator model Functional response Equilibrium points Stability Lyapunov function
Mathematics Subject ClassificationPrimary 92D40 Secondary 34D20 49K15 70K05
The authors would like to thank the anonymous referees for their extensive comments on the revision of the manuscript which really improved the quality of the paper. This research work is supported by University Grant Commission (UGC), Government of India to the author, Harsha Kharbanda (Sr. No. 2121440663).
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