Dynamic analysis of fractional-order singular Holling type-II predator-prey system

In this paper, a fractional-order singular (FOS) predator–prey model with Holling type-II functional response has been introduced, and the mathematical behavior of the model from the aspect of local stability is investigated. Through the fractional calculus and economic theory, a new and more realistic predator–prey model has been extended, and the solvability condition is presented. Besides, numerical simulations are considered to illustrate the effectiveness of the numerical method and confirm the theoretical results to explore the impacts of fractional-order and economic interest on the presented system in biological context. It is found that the presence of fractional-order in the differential model can improve the stability of the solutions and enrich the dynamics of system. In addition, singular models exhibit more complicated dynamics rather than standard models, especially the bifurcation phenomena, which can reveal the instability mechanism of systems.

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