On the existence and uniqueness of limit cycles for generalized Liénard systems
- Xiao, Dongmei
- Zhang, Zhifen
DOIAbstract
AbstractIn this paper, we consider a generalized Liénard systemdxdt=ϕ(y)−F(x),(0.1)dydt=−g(x), where F is continuous and differentiable on an open interval (b1,a1) with −∞⩽b1<0<a1⩽+∞. Assume that there exist a and b with b1<b<0<a<a1 such that xF(x)<0 as b<x<a, and xF(x)>0 as a<x<a1 or b1<x<b. A new uniqueness theorem of limit cycles for the Liénard system (0.1) is obtained. An example is given to show the application of the theorem
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