Lotka systems with directed dispersal dynamics: Competition and influence of diffusion strategies

• We explore the interplay of diffusion strategies and types of resource sharing.
• We identify cases when a stable coexistence equilibrium exists, and in certain cases prove its uniqueness.
• For most diffusion strategies, we justify the detrimental influence of faster diffusion, as well as of lower growth rates.
• We investigate the case of two locally stable semi-trivial equilibria.

We study a Lotka system describing two competing populations, and each of them chooses its diffusion strategy as the tendency to have a distribution proportional to a certain positive prescribed function. For instance, the standard diffusion corresponds to the choice of a uniform distribution. The paper is focused on the interplay of species competition and diffusion strategies. In the case when one of the diffusion strategies is proportional to the carrying capacity, while the other is not, and the competition does not discriminate the former species, we prove the competitive exclusion of the latter one. If the competition favors the latter species, there is still a range of parameters for which there is a coexistence, thanks to the better dispersal strategy chosen by the former species. The dependency on the interaction type, diffusion coefficients and intrinsic growth rates is explored. We prove that in the limit case, higher diffusion coefficients are detrimental while higher growth rates, as well as lower resources sharing, are beneficial for population survival.