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

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.