Bifurcation Analysis of a Class of Two-Delay Lotka–Volterra Predation Models with Coefficient-Dependent Delay

Xiuling Li and Haotian Fan ()
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Xiuling Li: College of Applied Mathematics, Jilin University of Finance and Economics, Changchun 130117, China
Haotian Fan: College of Applied Mathematics, Jilin University of Finance and Economics, Changchun 130117, China

Mathematics, 2024, vol. 12, issue 10, 1-22

Abstract: In this paper, a class of two-delay differential equations with coefficient-dependent delay is studied. The distribution of the roots of the eigenequation is discussed, and conditions for the stability of the internal equilibrium and the existence of Hopf bifurcation are obtained. Additionally, using the normal form method and the central manifold theory, the bifurcation direction and the stability for the periodic solution of Hopf bifurcation are calculated. Finally, the correctness of the theory is verified by numerical simulation.

Keywords: double time delay; Lotka-Volterra predation model; Hopf bifurcation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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