Limit cycles and invariant curves in a class of switching systems with degree four (Q1755695)

Consider a special planar polynomial system of degree four having \(y=0\) as a line of discontinuity and the conic \(x^2+ cy^2=1\), \(c\in\mathbb{R}\), as an invariant curve. The authors study the bifurcation of limit cycles from the origin with \(c\) as bifurcation parameter under the condition that the first eight Lyapunov constants vanish.