Local and global dynamics of a fractional-order predator-prey system\n with habitat complexity and the corresponding discretized fractional-order\n system

2019/06/04 by Shuvojit Mondal, Mondal, Shuvojit, M. Biswas +3
Mathematics · Medicine · #26A33 #34A08 #Advanced Differential Equations and Dynamical Systems #Dynamical Systems (math.DS) #FOS: Mathematics #Fractional Differential Equations Solutions #Mathematical and Theoretical Epidemiology and Ecology Models

paper · pdf · doi:10.48550/arxiv.1906.01206

openalex publication_date 2019/06/04 · openalex created_date 2022/07/29 · openalex updated_date 2026/07/28

Abstract

This paper is focused on local and global stability of a fractional-order\npredator-prey model with habitat complexity constructed in the Caputo sense and\ncorresponding discrete fractional-order system. Mathematical results like\npositivity and boundedness of the solutions in fractional-order model is\npresented. Conditions for local and global stability of different equilibrium\npoints are proved. It is shown that there may exist fractional-order-dependent\ninstability through Hopf bifurcation for both fractional-order and\ncorresponding discrete systems. Dynamics of the discrete fractional-order model\nis more complex and depends on both step length and fractional-order. It shows\nHopf bifurcation, flip bifurcation and more complex dynamics with respect to\nthe step size. Several examples are presented to substantiate the analytical\nresults.\n

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