Abstract
The dynamics of a general reaction–diffusion–advection two species model with nonlocal delay effect and Dirichlet boundary condition is investigated in this paper. The existence and stability of the positive spatially nonhomogeneous steady state solution are studied. Then by regarding the time delay \(\tau \) as the bifurcation parameter, we show that Hopf bifurcation occurs near the steady state solution at the critical values \(\tau _n(n=0,1,2,\ldots )\). Moreover, the Hopf bifurcation is forward and the bifurcated periodic solutions are stable on the center manifold. The general results are applied to a Lotka–Volterra competition–diffusion–advection model with nonlocal delay.
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Acknowledgements
Z. Li is supported by the Fundamental Research Funds for the Central Universities of Central South University (No. 2020zzts040), B. Dai is supported by the National Natural Science Foundation of China (No. 11871475) and R. Han is supported by the Youth Foundation of Zhejiang University of Science and Technology (No. XJ2021003203).
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Li, Z., Dai, B. & Han, R. Hopf Bifurcation in a Reaction–Diffusion–Advection Two Species Model with Nonlocal Delay Effect. J Dyn Diff Equat 35, 2453–2486 (2023). https://doi.org/10.1007/s10884-021-10046-w
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DOI: https://doi.org/10.1007/s10884-021-10046-w