Fractional-order delayed predator–prey systems with Holling type-II functional response

By Fathalla A. Rihan, Shanmugam Lakshmanan, A. Hashish, Rajan Rakkiyappan, E. Ahmed. 2015

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In this paper, a fractional dynamical system of predator–prey with Holling type-II functional response and time delay is studied. Local and global stability of existence steady states and Hopf bifurcation with respect to the delay is investigated, with fractional-order $$0< \alpha \le 1$$0<α≤1. It is found that Hopf bifurcation occurs when the delay passes through a sequence of critical values. Unconditionally, stable implicit scheme for the numerical simulations of the fractional-order delay differential model is introduced. The numerical simulations show the effectiveness of the numerical method and confirm the theoretical results. The presence of fractional order in the delayed differential model improves the stability of the solutions and enrich the dynamics of the model.

Subfields: Geometry and Topology, Modeling and Simulation, Public Health, Environmental and Occupational Health

View Paper: https://www.semanticscholar.org/paper/3a4be3eaa4c51db563691d0f8a8a817e662b9078