Abstract
In the present work, we mainly focus on a new established fractional-order predator-prey system concerning both types of time delays. Exploiting an advisable change of variable, we set up an isovalent fractional-order predator-prey model concerning a single delay. Taking advantage of the stability criterion and bifurcation theory of fractional-order dynamical system and regarding time delay as bifurcation parameter, we establish a new delay-independent stability and bifurcation criterion for the involved fractional-order predator-prey system. The numerical simulation figures and bifurcation plots successfully support the correctness of the established key conclusions.
Highlights
Setting up mathematical models to describe the natural phenomena has become an important topic in real life. e interaction of predator population and prey population plays a significant role in maintaining ecological balance in nature
Time delay often exists in biological systems due to the lag of the response of different predators and preys
Time delay will lead to the loss of stability, periodic oscillation, bifurcation, and chaotic behavior of predator-prey models. us, the study on the impact of time delay on dynamical nature of predator-prey models has attracted great interest of many scholars in the fields of biology and mathematics
Summary
Setting up mathematical models to describe the natural phenomena has become an important topic in real life. e interaction of predator population and prey population plays a significant role in maintaining ecological balance in nature. Alsakaji et al [4] made a detailed discussion on permanence, local and global stabilities, Hopf bifurcation, and a predatorprey model with time delay. Yuan et al [30] established a set of sufficient conditions to ensure the stability and the onset of Hopf bifurcation for a fractional-order predator-prey model. Wang et al [31] discussed the stability and bifurcation for a generalized fractional-order predator-prey system involving time delay and interspecific competition. The investigation on Hopf bifurcation of fractional-order delayed predator-prey systems merely involves discrete time delay. There are only very few works on Hopf bifurcation of predator-prey system involving distributed time delay. Inspired by the analysis above, we are to analyze the stability and Hopf bifurcation for fractional-order predatorprey model involving discrete time delay and distributed time delay.
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