A Class Of Cubic System With The Question Of Limit Cycles And Bifurcate

Recently many famous scholars were attracted to study the general liénard system equation with the question of it's limit cycle and bifurcate .When we append a thrice item to the quadratic system, the quadratic system become the cubic system .it is a interesting question whether their limit cycles near the origin exist some relations or not . In this paper, we discuss the uniqueness limit cycle and the question of bifurcate about a class of general Liénard equation in the system. That the system is when the signs of are equal in the system .We obtain the conclusion: Conclusion 1 when and or ,O(0,0) is the finite critical point .the system(1) has no limit cycles. Conclusion 2 under the conclusion , when the system　(1) has no limit cycles；when ,the system(1) has at most one limit cycles；when , the system(1) has no limit cycles；when ,the system(1) turn up the homoclinic.　In the end ,if we confine the coefficient b(),we will find the limit cycles of the cubic system (1) near the origin which varies with the parameter has the similar variable process with quadratic system (I)equation when...