A Lotka-Volterra Competition Model With Combined Harvest,Time Delay And Allee Effect

This paper discusses a Lotka-Volterra competition model with combined harvest and time delay,and one species subjects to Allee effect.Firstly,the local and global stability of the equilibrium point of the no time-delayed model is analyzed.The results of the study show that,according to different parameter areas,the two species are either coexistence or competitive exclusion.The solution of the model can reach the expected state by adjusting the initial value or the harvesting effort.This has certain guiding significance for preventing and controlling biological invasion and breeding rare speciesSecondly,the research also discusses the bifurcation situation of the model when two time delays are not equal to 0 at the same time.There exists a critical value of time delay,such that the equilibrium point is locally asymptotically stable when the delay is small than the critical value,and a Hopf bifurcation appears when the delay equal to the critical valueThirdly,the research analyzes the adaptive dynamic behavior of the model,and obtains the conditions for whether the mutant y species can successfully invade,as well as the conditions for the continuous stable strategy and evolutionary branch of the singular strategy m*.The population will change from monomorphic to polymorphic when the mutant population continues to undergo evolutionary branches,which is conducive to the creation of biodiversity.Finally,numerical method is also used to verify the results of analysis.