Asymptotic Behavior Of Two Types Of Stochastic Population Models

The environment where the population lives often has some random disturbances,which affect the change trend of the population.Therefore,the study of the population model under the random disturbances is of great significance to the management and protection of the population.Common disturbances in life are white noise,L′evy noise,colored noise,etc.Based on this,this paper mainly studies the asymptotic behavior of two types of population models under random disturbances.Chapter 1 introduces the research dynamics of random population model and gives the main contents of this paper.Chapter 2 concerns asymptotic behavior of a class of stochastic predator-prey model with delay and L′evy jumps.Firstly,the existence and uniqueness of the global positive solutions of this model are proved,and then according to the exponential martingale inequality and chebyshev inequality,the ultimate boundedness and extinction are proved.Finally,numerical simulation is used to verify the theoretical results.Chapter 3 discusses asymptotic behavior of stochastic mutualism model with Markov switching under environmental pollution.Firstly,the existence and uniqueness of the global positive solutions of the model are proved,and then the stochastic ultimate boundedness,extinction and average persistence of the model are proved according to chebyshev inequality and other methods.Finally,numerical simulation is used to verify the theoretical results.Finally,the results of this paper are summarized,and some ideas on the future research direction are provided.