Further Study on Dynamics for a Fractional-Order Competitor-Competitor-Mutualist Lotka–Volterra System

Abstract

On the basis of the previous publications, a new fractional-order prey-predator model is set up. Firstly, we discuss the existence, uniqueness, and nonnegativity for the involved fractional-order prey-predator model. Secondly, by analyzing the characteristic equation of the considered fractional-order Lotka–Volterra model and regarding the delay as bifurcation variable, we set up a new sufficient criterion to guarantee the stability behavior and the appearance of Hopf bifurcation for the addressed fractional-order Lotka–Volterra system. Thirdly, we perform the computer simulations with Matlab software to substantiate the rationalisation of the analysis conclusions. The obtained results play an important role in maintaining the balance of population in natural world.