Stability and Hopf bifurcation of a heterogeneous diffusive model with spatial memory. (English) Zbl 1535.35015
This paper reports the stability analysis and the Hopf bifurcation of a single advection-diffusion population model. The model involves the spatial memory effect, maturation delay effect and the spatial heterogeneity. The biological meaning of the diffusive model is sound and the yielded theoretical result is wealthy. Interestingly, the authors found that large diffusion may not lead to multiple stability switches of a spatially heterogeneous single population model with interactions of two maturation-memory density dependence delays in the spatial memory environment. Overall, the obtained results may be useful to figure out the dynamic profiles of a single population model in the spatial memory and heterogeneous environments.
Reviewer: Mengxin Chen (Xinxiang)
MSC:
| 35B32 | Bifurcations in context of PDEs |
| 35K20 | Initial-boundary value problems for second-order parabolic equations |
| 35K57 | Reaction-diffusion equations |
| 35R10 | Partial functional-differential equations |
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