The Selection Mechanism Of Minimum Wave Velocity For Nonlinear Lotka-Volterra Competitive Models

It is well known that competing scenarios for different species create the biodiversity of ecosystems.When a certain kind When a group spreads,it encounters other populations,and the dispersal of that population grows for other populations in competition There are also important implications from a biological point of view,in the invasion of two species that have competitive exclusion and spatial dispersal In the system,interactions between invasive and resident species lead to ecological balance and therefore a large number of organisms Mathematicians have made the study of invasion dispersal behavior the focus of modern population dynamics.In addition,research people They also found that the invasion spread behavior is the ubiquitous traveling wave phenomenon of nature.Not only that,traveling wave phenomena are also distributed in many scientific fields,such as biophysics,population genetics,and numbers Studied ecology,chemistry,physics,etc.Because of the profound background significance of traveling waves in these natural processes,Therefore,it is particularly necessary to find the traveling wave solution theoretically and study its dynamic properties.In biomathematics,the logistic equation is used to describe the population growth of a single species,as for Lot.ka-Volterra Models are often used to describe the dynamics of ecosystems in which two species interact,from mathematical models Angle analysis found that two species spread spatially in a certain direction at a constant speed,while their own shape When the pattern remains unchanged or changes regularly,it leads to the occurrence of traveling wave phenomenon,and its diffusion speed can be used Wave solution to describe.In order to further describe the diffusion phenomenon of invasive species to resident species,this paper qualitatively analyzes the nonlinear Lotka-Volterra system based on the theory of dynamical system,and analyzes the local dynamics of the model through the local behavior of the equilibrium point.For Lot.kaVolterra systems,the traveling wave soluion is the solution that connects two equilibrium states,and so far,there have been many research results on the traveling wave solution,including its existence,and exponential decay behavior at infinity.The main problem studied in this paper is the traveling wave phenomenon of the nonlinear Lotka-Volterra competitive diffusion model Traveling wave solution minimum wave velocity selection mechanism.The main research idea is for three types of nonlinear Lotka-Volterra The competitive diffusion system model gives its corresponding collaborative system,and the minimum wave velocity of the traveling wave solution of the cooperative system is studied Selection mechanism(linear vs.nonlinear).The difficulty in studying is to construct a suitable upper and lower solution form and use the upper and lower solution formulas The method combines monotonic iteration techniques to prove the existence of traveling wave solutions with exponential decay,and further establishes a series of primaries The nature of the solution of the value system.In addition,using the comparison principle and the attenuation characteristics of the traveling wave,linear or nonlinear is obtained.The general conditions of the propagation speed are selected,and then according to the critical value of the propagation speed,the speed selection is derived Clear parameter conditions.The innovation of this paper is to expand the research scope of competitive equations from integer low-order to p+1 higher-order equations without violating the actual biological significance.However,due to the complexity of the nonlinear selection of velocity in the p+1 power equation,this paper only discusses the general conditions and explicit conditions of linear velocity,leaving a theoretical basis for subsequent research.