Cyclicity of <inline-formula><tex-math id="M1">\begin{document}$ (1,3) $\end{document}</tex-math></inline-formula>-switching FF type equilibria

Abstract

Hilbert's 16th Problem suggests a concern to the cyclicity of planar polynomial differential systems, but it is known that a key step to the answer is finding the cyclicity of center-focus equilibria of polynomial differential systems (even of order 2 or 3). Correspondingly, the same question for polynomial discontinuous differential systems is also interesting. Recently, it was proved that the cyclicity of $ (1, 2) $-switching FF type equilibria is at least 5. In this paper we prove that the cyclicity of $ (1, 3) $-switching FF type equilibria with homogeneous cubic nonlinearities is at least 3.