Hopf Bifurcation Of A Competing Syste

This thesis studies the Hopf bifurcation in three types of three-dimensional competitive systems,i.e.,Lotka-Volterra,Ricker and Leslie-Gower systems.By accurate calculation or qualitative proof,we obtain the existence and stability of 2-order fine focus in Zeeman’s classes 26-31.Then we use the Hopf bifurcation theory and Poincare-Bendixson theorem to discuss the multiplicity of limit cycles in these systems,and getting their stability and bifurcation direction.By studying 15 kinds of three-dimensional competitive systems,we learns that the lower bound of the number of limit cycles is:#12 The results about classes 28 and 30 in Lotka-Volterra system,Ricker system,Leslie-Gower system are new.