Birth of limit cycles from a 3D triangular center of a piecewise smooth vector field
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Abstract
We consider a piecewise smooth vector field in R3, where the switching set is on an algebraic variety expressed as the zero of a Morse function.We depart from a model described by piecewise constant vector fields with a non-usual center that is constant on the sliding region. Given a positive integer k, we produce suitable nonlinear small perturbations of the previous model and we obtain piecewise smooth vector fields having exactly k hyperbolic limit cycles instead of the center. Moreover, we also obtain suitable nonlinear small perturbations of the first model and piecewise smooth vector fields having a unique limit cycle of multiplicity k instead of the center. As consequence, the initial model has codimension infinity. Some aspects of asymptotical stability of such system are also addressed in this article.
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Bifurcation, Limit cycles, Periodic solutions, Piecewise smooth vector fields
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English
Citation
IMA Journal of Applied Mathematics (Institute of Mathematics and Its Applications), v. 82, n. 3, p. 561-578, 2017.
