In this paper, we are concerned about smoothing of a class of
$\Sigma$-polycycles of Filippov systems, namely homoclinic-like connections to
regular-tangential singularities. Conditions are stablished in order to
guarantee the existence of limit cycles bifurcating from such connections.Comment: arXiv admin note: text overlap with arXiv:2003.0954

Novaes, Douglas D.

Rondón, Gabriel

English

arXiv

In this paper, we are concerned about smoothing of Filippov systems around
homoclinic-like connections to regular-tangential singularities. We provide
conditions to guarantee the existence of limit cycles bifurcating from such
connections. Additional conditions are also provided to ensured the stability
and uniqueness of such limit cycles. All the proofs are based on the
construction of the first return map of the regularized Filippov system around
homoclinic-like connections. Such a map is obtained by using a recent
characterization of the local behaviour of the regularized Filippov system
around regular-tangential singularities. Fixed point theorems and
Poincar\'{e}-Bendixson arguments are also employed.Comment: arXiv admin note: text overlap with arXiv:2003.0954

Smoothing of homoclinic-like connections to regular tangential singularities in Filippov systems

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