Research On Spatiotemporal Dynamics Of The Leslie-Gower Type Predator-Prey System

Predation relationship is an important relationship in biological communities,and it is also the connection foundation of complex food chains,food networks,and biochemical network structures.The stability of the population of the predator-prey system based on the predation relationship has a significant impact on the stability and diversity of the ecosystem.The population of the predator-prey system is not only influenced by its internal mechanisms,such as the predatory effect,fear effect,and refuge effect,but also by environmental toxins caused by human activities.The predator-prey dynamics model is an important tool for characterizing the population distribution,revealing the law of its evolution,and predicting its trends of development.The Leslie-Gower type population model is one of the important models.It is of great significance to study the effects of the above factors on the spatiotemporal distribution and periodic oscillation dynamic behavior of the population of Leslie-Gower type predator-prey system through Hopf and Turing bifurcation,and predict the changing trends of their population.This study provides a scientific basis for protecting endangered species and maintaining the diversity and stability of ecosystems.The main research contents are as follows:(1)Leslie-Gower type reactive diffusion predator-prey model with refuge and nonlocal nonlocal predation effects was established,and the Turing instability conditions of the model were given.The evolution of the Turing pattern of the prey with the delay and refuge effects was demonstrated through numerical simulation.The results indicate that the nonlocal predation effect promotes the growth of the prey population and is beneficial for its survival;the relatively strong refuge effect has a protective effect on the prey and can promote the persistence of the system.(2)A Leslie-Gower type delayed predator-prey reaction diffusion model with fear and refuge effects was established,and the conditions of stability switching,Hopf bifurcation,and Turing instability the model were given.Numerical simulations show the stable solution and periodic solution with time and spcace within the stability switching intervals,as well as the Turing pattern induced by fear intensity and refuge effect.Finally,the dynamic behavior of the delayed systems and the delayed diffusion systems was compared.The results indicate that:(1)The smaller the delay of the fear response,the larger the amplitude of the periodic solution oscillation of the system,which is less conducive to system stability.(2)The number of prey populations decreases with the increase intensity of the fear,which means that the greater intensity of the fear,the less conducive it is to the survival of the prey.(3)A small number the prey sheltered bait helps to stabilize the bait population.While the number of the prey sheltered in shelters exceeds a certain value,the prey population decreases.(4)The diffusion behavior of the population contributes to system stability.(3)A Leslie-Gower type delayed predator-prey reaction diffusion model with toxins in the environment was established,and the Hopf bifurcation and Turing instability conditions of the model were given.Numerical simulations show the stable solution and periodic solution with time and spcace,as well as Turing patterns induced by the intensity of environmental toxins on predators.Finally,the dynamic behavior of the delayed system and the delayed diffusion systems was compared.The results indicate that the greater the toxin intensity and toxin deposition delay,the less conducive it is to system stability;Population diffusion behavior contributes to system stability.(4)A Leslie-Gower type predator-prey reaction diffusion model with interval parameters was established.Turing instability conditions of the model were given,and pattern selection of the modelwas obtained through multi-scale analysis.Pattern selection behavior was verified through numerical simulations,and Turing patterns of the prey induced by diffusion coefficient and the conversion rate of the prey to predator biomass was obtained.The main results indicate that when the system parameters are interval parameters,the control parameters are also interval numbers,and the left and right endpoints of the pattern selection interval are interval numbers;The influence of different interval parameters on the pattern formation and population the the system varies.