Hopf bifurcations in a class of reaction-diffusion equations including two discrete time delays: An algorithm for determining Hopf bifurcation, and its applications

Ş. Bilazeroğlu and H. Merdan

Chaos, Solitons & Fractals, 2021, vol. 142, issue C

Abstract: We analyze Hopf bifurcation and its properties of a class of system of reaction-diffusion equations involving two discrete time delays. First, we discuss the existence of periodic solutions of this class under Neumann boundary conditions, and determine the required conditions on parameters of the system at which Hopf bifurcation arises near equilibrium point. Bifurcation analysis is carried out by choosing one of the delay parameter as a bifurcation parameter and fixing the other in its stability interval. Second, some properties of periodic solutions such as direction of Hopf bifurcation and stability of bifurcating periodic solution are studied through the normal form theory and the center manifold reduction for functional partial differential equations.

Keywords: Hopf bifurcation; Functional partial differential equations; Reaction-diffusion system; Delay differential equations; Stability; Periodic solutions; Discrete time delays (search for similar items in EconPapers)
Date: 2021
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Citations: View citations in EconPapers (5)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:142:y:2021:i:c:s0960077920307852

DOI: 10.1016/j.chaos.2020.110391

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