Global stability and Hopf bifurcation of a delayed cooperative species model with density-dependent diffusion. (English) Zbl 1507.35026
Summary: In this article, we have proposed a newly delayed cooperative species model with density-dependent diffusion. Firstly, we prove the existence and uniqueness of positive equilibrium of this model through mathematical analysis method. Then, for this model, we investigate the persistence properties in the case of self-diffusion and global stability of positive equilibrium by constructing Lyapunov function. Further, we discuss the existence problem of Hopf bifurcation deduced by delay. Finally, the theoretical results in this article are verified by carrying out some numerical simulations. The research results show that density dependent diffusion does not affect the stability of the positive equilibrium of the model, but delay does.
MSC:
| 35B32 | Bifurcations in context of PDEs |
| 35B35 | Stability in context of PDEs |
| 35K51 | Initial-boundary value problems for second-order parabolic systems |
| 35K57 | Reaction-diffusion equations |
| 92D25 | Population dynamics (general) |
Keywords:
cooperative species model; density-dependent diffusion; delay; global stability; Hopf bifurcationReferences:
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