Effects of anisotropic diffusion on the dynamics of a predator-prey system in heterogeneous environments

We investigate a predator-prey model within two-dimensional heterogeneous environments under no-flux boundary conditions. The populations are assumed to undergo horizontal and vertical movements with varying probabilities, representing different dispersal strategies. In contrast to random diffusion systems, this system exhibits increased complexity in its dynamics. Anisotropic diffusion offers a broader range of possibilities, enabling the prey to more effectively adapt to available resources. We examine the stability of the semitrivial solutions through eigenvalue analysis and abstract persistence theory. By employing degree theory and bifurcation theory, we establish the existence of positive steady states in this system. Furthermore, our numerical results offer valuable insights and intuition for further research.