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Hopf bifurcation in a Lotka-Volterra competition-diffusion-advection model with time delay
In this paper, we mainly investigate a Lotka-Volterra competition-diffusion-advection system with time delay, where the diffusion and advection rates of two competitors are different. By employing the Lyapunov-Schmidt reduction method, we obtain the existence of steady state solution. A weighted inn...
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Published in: | Journal of Differential Equations 2023-01, Vol.344, p.74-101 |
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Main Authors: | , |
Format: | Article |
Language: | English |
Subjects: | |
Citations: | Items that this one cites Items that cite this one |
Online Access: | Get full text |
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Summary: | In this paper, we mainly investigate a Lotka-Volterra competition-diffusion-advection system with time delay, where the diffusion and advection rates of two competitors are different. By employing the Lyapunov-Schmidt reduction method, we obtain the existence of steady state solution. A weighted inner product has been introduced to study stability and Hopf bifurcation at the spatially nonhomogeneous steady-state. Our results imply that the infinitesimal generator associated with the linearized system have two pairs of purely imaginary eigenvalues, and time delay can make the spatially nonconstant positive steady state unstable for a reaction-diffusion-advection model. In addition, the bifurcation direction and stability of Hopf bifurcating periodic orbits was obtained by means of the center manifold reduction and the normal form theory. |
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ISSN: | 0022-0396 1090-2732 |
DOI: | 10.1016/j.jde.2022.10.037 |