Mathematical Model Analysis of Animal Population Movement and Diffusion
Diffusion is one of the most important events in animal life history, which can promote the succession of biological communities and increase species diversity. In terms of ecology and genetics, there are also some differences in the definition of diffusion. Ecological diffusion refers to the movement of individuals from one place to another, while genetic diffusion refers to the successful reproduction of individuals from one reproductive population to another. Ecological diffusion emphasizes processes, mainly considering the distribution and abundance of organisms, while genetic diffusion emphasizes the genetic structure of populations and the level of gene exchange among populations. Zoological studies have shown that the survival probability of wildlife depends on the diffusion of animals to find, adapt and settle in new habitats. In this paper, we mainly summarize the research on animal movement and growth diffusion in history, and briefly introduce the relevant preparatory knowledge about stability of differential equations which will be applied in this paper. The mathematical model of animal cluster motion and its synchronization in motion are studied. The key of building cluster motion model is to build the renewal mode of individual motion angle. Finally, the diffusion of grasshoppers in limited cropland is taken as an example to study the diffusion of animal population under limited and irrecoverable environment.