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In this paper, we investigate a delayed reaction–diffusion–advection equation, which models the population dynamics in the advective heterogeneous environment. The existence of the nonconstant positive steady state and associated Hopf… Click to show full abstract
In this paper, we investigate a delayed reaction–diffusion–advection equation, which models the population dynamics in the advective heterogeneous environment. The existence of the nonconstant positive steady state and associated Hopf bifurcation are obtained. A weighted inner product associated with the advection rate is introduced to compute the normal forms, which is the main difference between Hopf bifurcation for delayed reaction–diffusion–advection model and that for delayed reaction–diffusion model. Moreover, we find that the spatial scale and advection can affect Hopf bifurcation in the heterogenous environment.
Journal Title: Journal of Dynamics and Differential Equations
Year Published: 2019
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