In this paper we study a model of plant-herbivore systems. Sufficient and necessary conditions for the globally asymptotic stability of the positive equilibrium points and for the existence of unique stable limit cycle are obtained. We have also obtained a global bifurcation curved surface.
Sufficient conditions for the global stability of the positive equilibrium points and for the existence of unique stable limit cycle are obtained when d1 = d2.
In this Paper,we prove the acymptic stability of an infectious disease ,ty-namics ordinary differential equation at the positive equilibrium points and by use of the bifurcation theory prove that there exists no small amplitude peridic solution at the positive e-quilibrium points.
The stability of dynamic model equilibrium for lifelong immunity infections was studied. The small amplitude periodic solution at the positive equilibrium points was proved by using Hopf theory.
Some qualitative properties of the third kind of functional reaction model of prey species having constant stored rate in restricted density prey-predatory system are studied. Firstly,the existence for the positive equilibrium points and their properties are discussed. Secondly,some conditions for the nonexistence of limit cycle by Dulac function are given.
In this paper we study a model of plant-herbivore systems. Sufficient and necessary conditions for the globally asymptotic stability of the positive equilibrium points and for the existence of unique stable limit cycle are obtained. We have also obtained a global bifurcation curved surface.
In this paper we study a kind of plant-Herbivore systems. Sufficient conditions for the global stability of the positive equilibrium points and for the existence of unique stable limit cycle are obtained when d1 = d2.
In this Paper,we prove the acymptic stability of an infectious disease ,ty-namics ordinary differential equation at the positive equilibrium points and by use of the bifurcation theory prove that there exists no small amplitude peridic solution at the positive e-quilibrium points.