Maximum Number of Limit Cycles for Generalized Kukles Polynomial Differential Systems
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DOI: 10.1007/s12591-016-0300-3
Abstract: We study the maximum number of limit cycles of the polynomial differential systems of the form $$\begin{aligned} \dot{x}=-y+l(x), \,\dot{y}=x-f(x)-g(x)y-h(x)y^{2}-d_{0}y^{3}, \end{aligned}$$x˙=-y+l(x),y˙=x-f(x)-g(x)y-h(x)y2-d0y3,where $$l(x)=\varepsilon l^{1}(x)+\varepsilon ^{2}l^{2}(x),$$l(x)=εl1(x)+ε2l2(x),$$f(x)=\varepsilon f^{1}(x)+\varepsilon ^{2}f^{2}(x),$$f(x)=εf1(x)+ε2f2(x),$$g(x)=\varepsilon g^{1}(x)+\varepsilon ^{2}g^{2}(x),$$g(x)=εg1(x)+ε2g2(x),$$h(x)=\varepsilon h^{1}(x)+\varepsilon ^{2}h^{2}(x)$$h(x)=εh1(x)+ε2h2(x) and $$d_{0}=\varepsilon d_{0}^{1}+\varepsilon ^{2}d_{0}^{2}$$d0=εd01+ε2d02 where $$l^{k}(x),$$lk(x),$$f^{k}(x),$$fk(x),$$g^{k}(x)$$gk(x)… read more here.
Keywords: number; maximum number; number limit; limit cycles ... See more keywords