Two problems about pseudolinear systems
The subject of this note are generalized Liénard systems \(\dot x = a(x) + b(y)\), \(\dot y = c(x) + d(y)\), where the right hand side is differentiable in \(\mathbb{R}^ 2\) and the origin is the only equilibrium. In answering a question asked by R. Conti, the author presents examples of such systems for which a) the origin is a center-focus, i.e., in any neighborhood of the origin, there are both closed and nonclosed orbits; b) the origin belongs to the \(\omega\)-limit set of each point \((x,y) \in \mathbb{R}^ 2\), but is not globally attractive; c) the origin is globally attractive and unstable.
scientific article; zbMATH DE number 682127
scientific article