Types Of Three-dimensional System Of Bifurcation Of Limit Cycles

The limit cycle bifurcation of a few kinds of Three-dimension systems are considered in this paper. Some background knowledge, the state of study and some theorem are introduced in the first chapter. A kind of Three-dimension system with mixed-perturbation are considered in the second chapter by using the theorem of center manifold and bifurcation theory of planar system, How can the Three-dimension use the theorem of center manifold are discussed, the conditions of the existence of the limit cycle are provided, and the conclusions of Zhou Yicang are bettered. The existence of the limit cycle of a special Three-dimension system is discussed in the third chapter by using the theorem of center manifold and the first order Hopf bifurcation theorem. The three degree system of two-dimension manifold decreasing dimension from the three-dimension system include all parameters situation which Ma Zhien, Chen Lansun, Jin Tieying, Yang Yujun discussed. A kind of special Three-dimension system is studied using the theorem of center manifold and Melnikov function. the sufficient conditions of the limit cycle bifurcated from homoclinic orbit are provided. The conclusions of Jin Yinlai and Zhuang Weixin are completed.