Analysis Of Population Dynamics Based On Stochastic Lotka-Volterra Model

The development and progress of society have prompted the improvement of the consciousness of ecological civilization,which has also greatly promoted people's close attention to the natural ecology.In particular,the survival and development of the population has become more and more hot topics of concern and research all over the world.Therefore,based on the Lotka-Volterra model,a stochastic mutualistic parasite-host model with Lévy-jumps,an optimal harvesting policy for a stochastic mutualism parasite-host model with Lévy-jumps,and a stochastic cooperative system with pulse environmental toxicant input and periodic implulses separately are established.Firstly,the survival threshold of a stochastic mutualistic parasite-host model with Lévy-jumps is given,and an important result is obtained that environmental white noise and Lévy-jumps have a very important influence on the size of the population.In addition,sufficient conditions for the stability of the system are established.Secondly,an optimal capture strategy for a stochastic mutualism parasite-host system with Lévy-jumps is established,and the optimal harvesting effort and the maximum sustainable yield are also obtained.Finally,the survival threshold of two species of the stochastic cooperative system with pulse environmental pollutants input and periodic implulses is obtained,and the global attraction to any positive solution of this system is given.In addition,the relevant conclusions of these three models are verified by numerical simulation respectively.The study of these models advances the exploration of the issue of population survival and development in the natural world,and provides a mathematical basis for further research.