Limit cycles and invariant cylinders for a class of continuous and discontinuous vector field in dimention 2n

Mauricio Firmino Silva Lima, Jaume Llibre

Research output: Contribution to journalArticleResearchpeer-review

4 Citations (Scopus)

Abstract

The subject of this paper concerns with the bifurcation of limit cycles and invariant cylinders from a global center of a linear differential system in dimension 2n perturbed inside a class of continuous and discontinuous piecewise linear differential systems. Our main results show that at most one limit cycle and at most one invariant cylinder can bifurcate using the expansion of the displacement function up to first order with respect to a small parameter. This upper bound is reached. For proving these results we use the averaging theory in a form where the differentiability of the system is not needed. © 2011 Elsevier Inc. All rights reserved.
Original languageEnglish
Pages (from-to)9985-9996
JournalApplied Mathematics and Computation
Volume217
Issue number24
DOIs
Publication statusPublished - 15 Aug 2011

Keywords

  • Continuous piecewise linear vector fields
  • Discontinuous piecewise linear vector fields
  • Equilibrium point
  • Invariant cylinder
  • Limit cycle
  • Periodic orbit

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