Generating Shilnikov chaos in 3D piecewise linear systems
作者：
Highlights：
• Our method to construct chaotic piecewise linear systems with two variants: One with homoclinic and the other with heteroclinic chaos. Our construction algorithm combines hyperbolic and nonhyperbolic linear domains, e.g. focus-saddle and center-node.
• Unlike previous results our proposed method constructs homoclinic and heteroclinic orbits by combining focus-saddle and center-node linear domains by establishing crossing exit and return points on the switching surface based on the geometry of their stable and unstable eigenspaces.
• Is important to notice that by construction there is a large set of parameter values that satisfies the restriction our method for Shilnikov chaos.
摘要
•Our method to construct chaotic piecewise linear systems with two variants: One with homoclinic and the other with heteroclinic chaos. Our construction algorithm combines hyperbolic and nonhyperbolic linear domains, e.g. focus-saddle and center-node.•Unlike previous results our proposed method constructs homoclinic and heteroclinic orbits by combining focus-saddle and center-node linear domains by establishing crossing exit and return points on the switching surface based on the geometry of their stable and unstable eigenspaces.•Is important to notice that by construction there is a large set of parameter values that satisfies the restriction our method for Shilnikov chaos.
论文关键词：Chaotic dynamics,Homoclinic/heteroclinic orbits,Linear time-invariant systems
论文评审过程：Received 29 April 2020, Revised 14 October 2020, Accepted 6 December 2020, Available online 23 December 2020, Version of Record 23 December 2020.
论文官网地址：https://doi.org/10.1016/j.amc.2020.125877
