Dynamics Of A Class Of Non-continuous Predator-Prey Systems At The Right End

Any species in nature is not isolated,and the populations are interconnected and interact.Any population has a distinct life stage with different age structures.The juvenile and adult individuals of the population have completely different foods,different living spaces,and different evacuation characteristics,which are particularly evident in insects and amphibians.In recent years,most scholars have studied the age-structured predator-prey model and obtained many valuable results,but it is rare to use the discontinuous system to study the age-structured predator-prey system.In the real world,there are a lot of discontinuous dynamic behaviors.Most scholars often ignore or ignore the discontinuity factors when studying these problems,so the dynamic model can not accurately predict and explain the actual problems.Based on the previous studies,this paper mainly studies the age-structured predator-prey system with discontinuous application,and the following results are obtained:（1）Using the theory of discontinuous differential equations at the right end to establish a predator-prey model with age structure under discontinuous application.The model only considers the effect of discontinuous application on the prey,regardless of discontinuous application to the predator.Impact;（2）Using the differential inclusion theory of the right-end discontinuous system,the generalized Lyapunov theory and the La Salle-type invariant principle,the definition of the solution of the age-structured predator-prey system under discontinuous application and the positive solution are given.And boundedness;（3）The local asymptotic stability,global asymptotic stability of the equilibrium point of the discontinuous system and the convergence of the equilibrium point in finite time are studied.The specific time when the system reaches and stays at the equilibrium point is given,and the discontinuity is discussed.The effect of application on system balance.The results show that whenR₀<1,the equilibrium pointE₀ is globally asymptotically stable;when ₀R>1,it becomes unstable;when e,the positive equilibrium point f It is globally asymptotically stable.The research in this paper shows that:,₀R=1 is the critical value of the extinction of the prey.To achieve ecological balance of the discontinuous predator-prey system,the value of ₀R should be increased so that ₀R>1,so that?（0）<k₁（initial applicationrate）,find the most suitable?（0）,making the system ecologically balanced.