Study On Nonlinear Pattern Dynamics And Functions Of Two Predator-prey Models

Population is an important part of ecosystem,and the study of the pattern of the population system will be beneficial to us for understanding the impact on the population system brought by various elements of the ecosystem.To a certain extent,it can provide some suggestions been used to control the balance between organisms.Based on the above ideas,several types of population models have been established with the thorough comprehension of interaction between various factors within the population and the impact of human activities on the population.And we do some study on the pattern dynamics and function of predator-prey models with nonlinear factors.The main research contents are as follows:In Chapter 1,the current research background,research status of the ecological pattern and the main research contents of this dissertation are given.It summarizes the mechanism of pattern formation in the ecology,and the manifestation of specific mechanisms in reality.The significance and effect of the pattern existence in ecology are introduced,and the research on the pattern dynamics of populations at home and abroad is also introduced.In Chapter 2,in order to consider the impact of unpredictable disturbances on the ecosystem,a predator-prey model with Leslie-Gower and Beddington-De Angelis functional responses was established.And we introduced the unpredictable disturbances into the system as the form of feedback variables.It makes us to consider the role of feedback control in population models.Based on the analysis of the obtained Turing pattern,we find that the density of both populations decreases regardless of whether the feedback intensity to the prey or predator increases.The difference is that as the feedback intensity to the prey increases,the number of clusters of predator and prey all decrease,and the complexity of the pattern structure decreases.With the increase of the feedback intensity to the predators,although the number of each population is decreasing,the aggregation effect has occurred,the number of clusters has increased,more high-density points appear,and the complexity of the pattern structure increases.The ecological implications for the ecosystem are that feedback control variables with appropriate size will make the system more stable by providing a self-organizing structure.Properly sized feedback control variables will make the system more stable by providing a self-organizing structure.In Chapter 3,a reaction-diffusion model considering predation dependence and predator harvesting is established,and the effect of harvesting and predation dependence on population systems is studied.In order to reveal how the spatial distribution and population density change with changes in killing intensity and predation dependence,firstly the accurate Turing region is obtained by bifurcation analysis of Hopf and Turing.In addition,in order to explore the types of possible patterns,multi-scale analysis was performed to analyze the nonlinear behavior of the system and obtain the amplitude equations depicting Turing patterns.Subsequently,we alter the parameters which we are concerned in Turing domain to investigate how patterns transform.The results show that moderate predator harvesting can increase the population density,maintain the spatial structure of the population,and strengthen the stability of the ecosystem.When the harvesting intensity exceeds a critical value,the population density will decrease,and the pattern structure also lost,which weakens the stability of the system.When the predation dependence on prey increases,the population density and the complexity of the pattern are improved,the system becomes less vulnerable to damage,and the coexistence of the two species is promoted,which protects the species diversity of the ecosystem.In Chapter 4,we summarize and discuss the main research contents of this dissertation.