FAN Li1, SHI Zhong-ke1, CHEN Si-yang2
(1 College of Automation, Northwestern Polytechnical University, Xi′an 710069, Shaanxi, China; 2 College of Mathematics and Information Science, Shaanxi Normal University, Xi′an 710062, Shaanxi, China)
Abstract:
The dynamics of a class of non-symmetric Lienard equations are discussed. By analyzing the zeros of the Melnikov function, Hopf and homoclinic(heteroclinic) orbit bifurcations and stability are discussed.Furthermore, using Picard-Fuchs equations, it is proved that double limit cycle bifurcations occur between the degenerate Hopf and homoclinic bifurcation points. Moreover, a formula for calculating double limit cycle bifurcation is derived. Finally, the complete bifurcation diagrams and phase portraits are obtained.
KeyWords:
Lienard equation; bifurcation; bifurcation diagram; limit cycle
