Adaptive Dynamics Analysis Of Predator-prey Evolutionary Models With External Disturbance

In this paper,based on the theory and methods of adaptive dynamics,we establish two types of evolutionary dynamics model on predator phenotypic traits with external disturbance factors and investigate the influence of external disturbance factors on the evolution of predator phenotypic traits.In the first chapter,we introduce the background,history of the adaptive evolution on population phenotypic traits and introduce the main research work of this paper.In the second chapter,a Lotka-Volterra food chain evolutionary model with ex-ternal disturbance is established.First,the globally asymptotically stable condition of the positive equilibrium is obtained.Then we study the adaptive monomorphic dynamics and obtain the conditions of evolutionary singular strategy for evolutionary stability,con-vergence stability and evolutionary branching.Under the condition of the evolutionary branching,the adaptive dimorphic outcomes is obtained.Finally,by numerical simu-lations,we analyze the effects of external disturbance on the evolution of intermediate predator phenotypic traits.In the third chapter,we establish a two competitive prey-one predator evolution-ary model with external disturbance.First,we obtain the globally asymptotically stable condition of the positive equilibrium.Then the monomorphic and dimorphic evolution-ary dynamics is investigated by using the theory of adaptive dynamics.In particular,the conditions of evolutionary singular strategy for continuous stability and evolution-ary branching is obtained.Finally,we analyze the effects of external disturbance on the evolution of predator phenotypic traits by numerical simulations.In the last chapter,we summarize the main conclusions of this paper and discuss some problems which need to be studied further.