摘要
Applying Hopf bifurcation theory and qualitative theory, we show that the general cubic Lienard equations with quadratic damping have at most three limit cycles. This implies that the guess in which the system has at most two limit cycles is false. We give the sufficient conditions for the system has at most three limit cycles or two limit cycles. We present two examples with three limit cycles or two limit cycles by using numerical simulation.
Applying Hopf bifurcation theory and qualitative theory, we show that the general cubic Lienard equations with quadratic damping have at most three limit cycles. This implies that the guess in which the system has at most two limit cycles is false. We give the sufficient conditions for the system has at most three limit cycles or two limit cycles. We present two examples with three limit cycles or two limit cycles by using numerical simulation.
作者
Yu-quan Wang, Zhu-jun JingDepartment of Applied mathematics, College of Science, Nanjing Agricultural University, Nanjing 210095,ChinaDepartment of Mathematics, Hunan Normal University, Changsha 410081, China & Academy of Mathematicsand System Sciences, Chinese Academy of Sciences, Beijing 100080, China
基金
Supported by the National Natural Science Foundation of China
National Key Basic Research Special Found (No. G1998020307).
