Hopf bifurcation for a \(\varphi \)-Laplacian Liénard system
Consider the planar system \[ \dot x= y\varphi'(y),\;\dot y=-g(x)- f(x,a)y\tag{\(*\)} \] near the equilibrium point at the origin, where \(a\in\mathbb{R}^m\) is a parameter vector. \((*)\) is equivalent to the \(\varphi\)-Laplacian Liénard equation \[ (\varphi(x')'+ f(x,a) x'+ g(x)= 0. \] The authors determine the cyclicity of the origin (maximum number of limit cycles bifurcating from the origin) under some conditions on \(\varphi\), \(f\) and \(g\).
scientific article; zbMATH DE number 6891606