Hopf Bifurcation and Stability Analysis of a Fractional-Order Lotka-Volterra Predator-PreyModel with Two Delays

Mengfan Zhu; Zunshui Cheng; Youming Xin; Yun Shang; Xue Lin; Jinde Cao

doi:10.53941/ic.2026.100005

Abstract

This paper investigates the stability and Hopf bifurcation of a class of fractional-order Lotka-Volterra predator-prey models with two time delays. By selecting one time delay as the bifurcation parameter and fixing the other, the criterion for Hopf bifurcation induced by the corresponding time delay is derived. This paper also investigates the interaction between the two time delays via numerical simulations. The results show that the stability of the model can be either weakened or enhanced by appropriately adjusting the time delays. Finally, the feasibility of the proposed findings is verified through numerical examples.

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