Periodic sinks and periodic saddle orbits induced by heteroclinic bifurcation in three-dimensional piecewise linear systems with two zones

Lei Wang, Qingdu Li and Xiao-Song Yang

Applied Mathematics and Computation, 2021, vol. 404, issue C

Abstract: For general three-dimensional piecewise linear systems, some explicit sufficient conditions are achieved for the existence of a heteroclinic loop connecting a saddle-focus and a saddle with purely real eigenvalues. Furthermore, certain sufficient conditions are obtained for the existence and number of periodic orbits induced by the heteroclinic bifurcation, through close analysis of the fixed points of the parameterized Poincaré map constructed along the hereroclinic loop. It turns out that the number can be zero, one, finite number or countable infinity, as the case may be. Some sufficient conditions are also acquired that guarantee these periodic orbits to be periodic sinks or periodic saddle orbits, respectively, and the main results are illustrated lastly by some examples.

Keywords: Periodic orbits; Bifurcation; Stability; Periodic sinks; Periodic saddle orbits; Heteroclinic loops; Piecewise linear systems (search for similar items in EconPapers)
Date: 2021
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:404:y:2021:i:c:s0096300321002903

DOI: 10.1016/j.amc.2021.126200

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