Uniqueness of limit cycles for a class of Liénard systems (Q2767707)

Dynamic systems of Liénard type NEWLINE\[NEWLINE\dot{x} = \alpha(y) - \beta(y)F(x),\qquad \dot{y} = -g(x),NEWLINE\]NEWLINE are considered. Based on an estimate on the ``characteristic exponent of \(\gamma\)'' NEWLINE\[NEWLINE c(\gamma)= \int_0^T \operatorname {div} X(\gamma(t)) dt,NEWLINE\]NEWLINE sufficient conditions, that the above system has exactly one closed orbit, a hyperbolic stable limit cycle, are obtained. Here, \(X\) is a vectorial field plane and \(\gamma\) is a closed trajectory of \(X\) with period \(T\). Some examples give characteristic results in comparison with other articles.