Dynamical analysis of a diffusive population-toxicant model with toxicant-taxis in polluted aquatic environments. (English) Zbl 1543.35253
Summary: This paper deals with a diffusive population-toxicant model in polluted aquatic environments, with a toxicant-taxis term describing a toxicant-induced behavior change, that is, the population tends to move away from locations with high-level toxicants. The global existence of solutions is established by the techniques of the semigroup estimation and Moser iteration. Based on a detailed study on the properties of the principal eigenvalue for non-self-adjoint eigenvalue problems, we investigated the local and global stability of the toxin-only steady-state solution and the existence of positive steady state, which yields sufficient conditions that lead to population persistence or extinction. Finally, by numerical simulations, we studied the effects of some key parameters, such as toxicant-taxis coefficient, advection rate, and effect coefficient of the toxicant on population growth, on population persistence. Both numerical and analytical results show that a weak chemotaxis effect, a small advection rate of the population, and a weak effect of the toxicant on population growth are favorable for population persistence.
MSC:
| 35Q92 | PDEs in connection with biology, chemistry and other natural sciences |
| 92D25 | Population dynamics (general) |
| 92C17 | Cell movement (chemotaxis, etc.) |
| 35K57 | Reaction-diffusion equations |
| 35B32 | Bifurcations in context of PDEs |
| 35B35 | Stability in context of PDEs |
| 35P15 | Estimates of eigenvalues in context of PDEs |
| 35A01 | Existence problems for PDEs: global existence, local existence, non-existence |
| 35A02 | Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness |
Keywords:
population-toxicant model; toxicant-taxis; reaction-diffusion-advection system; bifurcation; stabilityReferences:
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