Bifurcation of Limit Cycles for 3D Lotka-Volterra Competitive Systems

Abstract

Bifurcation of limit cycles is discussed for three-dimensional Lotka-Volterra competitive systems. A recursion formula for computation of the singular point quantities is given for the corresponding Hopf bifurcation equation. Some new results are obtained for 6 classes 26---31 in Zeeman's classification, especially, an example with four limit cycles in class 29 is given for the first time. The algorithm applied here is effective for solving the above general cyclicity.