Periodic sinks and periodic saddle orbits induced by heteroclinic bifurcation in three-dimensional piecewise linear systems with two zones
作者：
Highlights：
• We achieve some explicit sufficient conditions for the existence of a heteroclinic loop connecting a saddle-focus and a saddle with purely real eigenvalues in a class of three-dimensional piece-wise linear systems.
• The number of newborn periodic orbits can be zero, one, finite number or countable infinity in different cases, which are richer than previous results involving only saddles with purely real eigenvalues, where such number can only be one.
• We not only reveal an important mechanism under which periodic orbits can be generated by heteroclinic bifurcation in non-smooth systems, but also give a way of constructing single-scroll periodic sinks or single-scroll saddle periodic orbits by using the simple piecewise linear systems.
摘要
•We achieve some explicit sufficient conditions for the existence of a heteroclinic loop connecting a saddle-focus and a saddle with purely real eigenvalues in a class of three-dimensional piece-wise linear systems.•The number of newborn periodic orbits can be zero, one, finite number or countable infinity in different cases, which are richer than previous results involving only saddles with purely real eigenvalues, where such number can only be one.•We not only reveal an important mechanism under which periodic orbits can be generated by heteroclinic bifurcation in non-smooth systems, but also give a way of constructing single-scroll periodic sinks or single-scroll saddle periodic orbits by using the simple piecewise linear systems.
论文关键词：Periodic orbits,Bifurcation,Stability,Periodic sinks,Periodic saddle orbits,Heteroclinic loops,Piecewise linear systems
论文评审过程：Received 15 May 2020, Revised 24 January 2021, Accepted 12 March 2021, Available online 1 April 2021, Version of Record 1 April 2021.
论文官网地址：https://doi.org/10.1016/j.amc.2021.126200
