Pattern Formation from Reaction–Diffusion Equation Using Discretization Method

We know that mathematics has wide applications in the areas of environmental science, medical science, ecology, biology, etc. One very useful term in the problem of prey–predator relation is the Lotka–Volterra predator–prey equation. Especially the differential equation plays a very important role in all areas of science. But it is also true that maximum biological and chemical problems are defined in form of some unknown functions. Here, in this paper, an environmental case involving two related populations of prey and predator species is discussed. As the classic Lotka–Volterra assumptions are imaginary, it is assumed that there is logistic behavior for both the existing species. We see that the number of two populations are too much dependent on each other.