Cyclicity of (1,3)-switching FF type equilibria

© 2019 American Institute of Mathematical Sciences. All rights reserved. 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.