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In a small tubular neighborhood of the heteroclinic orbits, we establish a local coordinate system by using the foundational solutions of the linear variational equation of the unperturbed system along the heteroclinic orbits. We study the bifurcation problems of twisted heteroclinic loop with resonant eigenvalues. Under the twisted conditions and some transversal conditions, we obtain the existence,...
In this paper, we present a method to compute focal values and periodic constants at infinity of a class of switching systems and apply it to study a cubic system. We prove that such a cubic system can have 7 limit cycles in the sufficiently small neighborhood of infinity. Moreover, we consider a quintic switching system to obtain 14 limit cycles at infinity, while continuous quintic systems can have...
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