Abstract
Our starting point is a discontinuous piecewise linear dynamical system in [Formula: see text] with two zones that present a single invisible two-fold straight line and invariant cylinders. We broke the dynamics of this vector field to obtain a new four-parameter piecewise linear vector field with a [Formula: see text]-singularity. For this vector field, we prove that the upper bound of simple crossing limit cycles (simple CLCs) is three, and provide conditions for the existence of 1, 2, or 3 simple CLCs. We also show the occurrence of three distinct bifurcations involving such simple CLCs that are derived from a bifurcation set with two parameters: (i) a Teixeira Singularity bifurcation (TS-bifurcation); (ii) a Fold bifurcation; and (iii) a Cusp bifurcation.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
