Mathematical Modelling And Analysis For Animal Population Movement And Diffusion

Motion and diffusion of animal is an important research area of Mathematical Biology.There’s a big difference between motion and diffusion.The study of both should use different mathematical methodsThis paper studies mathematical model of motion and diffusion of animal,The main contents are as follows:The main content of the first chapter is a summarize about research on increase and diffusion of animal in history, and a give a brief introduction on preparation knowledge of stability of differential equations.The second chapter studied the mathematical model of animal cluster’s motion and its synchronism. The key to establish the mathematical model of animal cluster’s motion is to establish update mode of individual’s movement angle.In this chapter we established update mode of angle in both cases.First,Local perception model was set up:In order to study the synchronism of model(2.4),we proved the following theorem through some properties of connectivity matrix.Theorem 2.4 For the model(2.4),if the cluster is connected according to e at0 t moment, and0 v satisfy the following condition:Finally,The system will have synchronism.Then, Overall perception model(2.7) was set up:We still have the following theorem for its synchronism:Theorem 2.4 For the model(2.7), there ia a0a,the following conclusion is true for all i(1￡i ￡N) :()0limi kThe third chapter mainly discussed changes of population area, On the premise of number of individual animal increase according to Logistic model.The fourth chapter discussed diffusion of animal population under a special case :the environment is limited. First we discussed how two populations effect on eachother in the diffusion of them, the following model was set up:The following theorem was proved to be rightTheorerm is the only asymptotic stability of equilibrium point of equation set(4.6).Finally, taking the diffusion of locusts in a limited area of crops as an example,we studied the diffusion of animal population in case of environment is limited and can not be resumed...