On Hopf cyclicity of planar systems (Q1570204)

By using the first-order Melnikov function with multiple parameters, the author investigates the problem of finding the maximal number of limit cycles in the Hopf bifurcation for a disturbed plane system of the form \[ \dot x=f(x) +\epsilon g(x,\epsilon,a), \] where \(x\in\mathbb R^2\), \(\epsilon \in R\), \(a \in D \subset \mathbb R^ n\) with \(D\) bounded, \(n\geq 1,\) and \(f, g\) are \(C^\infty\) functions. Some applications to the nonlinear and polynomial systems of Liénard type are discussed.