GLOBAL DYNAMICS AND PATTERN FORMATION IN A DIFFUSIVE POPULATION-TOXICANT MODEL WITH NEGATIVE TOXICANT-TAXIS

Because of the significance of remediating contaminated ecosystems, many mathematical models have been developed to describe the interactions between populations and toxicants in polluted aquatic environments. These models typically neglect the consequences of toxicant-induced behavioral changes on population dynamics. Taking into account that individuals may flee from areas with high toxicant concentrations to areas with low toxicant concentrations in order to improve their chances of survival, growth, and reproduction, we develop a diffusive population-toxicant model with toxicant-taxis. We establish the global well-posedness of our model and prove the global stability of spatially homogeneous toxicant-only steady states and population-toxicant coexistence steady states under some conditions. We find conditions under which stable spatially inhomogeneous steady states become unstable to trigger spatial pattern formations as the toxicant-taxis is strong. We also identify a narrow parameter regime in which toxicant-only and population-toxicant coexistence steady states are bistable. Numerical simulations are performed to illustrate that spatial aggregation and segregation patterns between the population and the toxicant will typically emerge. Our study highlights the important effects of toxicant-induced movement responses on the spatial distributions of populations in polluted aquatic environments.

Automated summary

Due to the importance of remediating contaminated ecosystems, numerous mathematical models have been developed to describe the interactions between populations and toxicants in polluted aquatic environments. However, these models often neglect the effects of toxicant-induced behavioral changes on population dynamics. In this study, we develop a diffusive population-toxicant model with toxicant-taxis, taking into account the possibility of individuals fleeing from high toxicant concentrations to low toxicant concentrations. We analyze the global well-posedness and stability of steady states under different conditions, and find that spatial pattern formations and bistable steady states may occur when the toxicant-taxis is strong. Our numerical simulations demonstrate the emergence of spatial aggregation and segregation patterns between populations and toxicants, illustrating the significant effects of toxicant-induced movement responses on the spatial distributions of populations in polluted aquatic environments.