Weak Competition and Ideally Distributed Populations in a Cooperative Diffusive Model with Crowding Effects

We study a dynamic model describing the cooperation-competition between two species, where the first species diffuses along a smooth distribution function while the second is dispersive randomly. The analysis is designed for weak competition with corresponding coefficients and by considering different resource functions. It is shown that the directed diffusion population has evolutionary advantages to design its own niche. The higher carrying capacity is an important issue of persistence. If there is a combination of two strategies adopted by the two species then the ideal free distribution is attained and the coexistence steady state is a global attractor.