The Poincaré Bifurcation Of Three-Species Competition Model

In this paper,we mainly consider the number of limit cycles of 3-dimensional Lotka-Volterra system(?)on its carrying simplex,where ri,ai,bi,ci,1 ?i?3 are all positive real numbers.In this paper,we introduce some existing Poincaré bifurcation formulas for 3-dimensional systems,and obtain new Poincaré bifurcation formulas(that is,to esti-mate the number of zeros of the corresponding Abelian integral).By applying the new Poincaré bifurcation formula to the above system,a 3-dimensional Lotka-Volterra competitive system can be obtained,which has at least two limit cycles on the corre-sponding carrying simplex.