Fractional order system dynamical behaviors with Beddington-DeAngelis functional response

Abstract

The present study proposes a fractional order prey-predator model with Beddington-DeAngelis functional response, that the Caputo fractional derivative is applied. There is exploration of the solutions' existence, uniqueness, non-negativity, and boundedness. Stability of all feasible equilibrium points is determined locally by the use of Matignon's condition. Moreover, the researchers also provide sufficient conditions to assure global asymptotic stability for both the predator-extinction equilibrium point and the positive equilibrium point, with selecting a relevant Lyapunov function and the incidence ofHopf-bifurcation is also displayed. Finally, the fractional order effect on the stability behavior of systems is investigated theoretically and also illustrated numerically to support theoretical results. © 2022 Production by the University of Garmian. This is an open access article under the LICENSE https://creativecommons.org/licenses/by-nc/4.0/