Nonlinear Dynamics

, Volume 93, Issue 4, pp 2445–2459 | Cite as

Homoclinic orbits and an invariant chaotic set in a new 4D piecewise affine systems

  • Qigui YangEmail author
  • Kai Lu
Original Paper


It is a challenging task to prove mathematically the existence of homoclinic orbits in a high-dimensional dynamical system. Here we first introduce a new four-dimensional (4D) piecewise affine system and then establishes useful yet general conditions on the existence of an orbit homoclinic to a spiral saddle-foci and chaos in the system. Rigorously mathematical analysis is also provided. A 4D example with both a homoclinic orbit and an invariant chaotic set is used to depict the effectiveness of analysis and prediction.


Chaos Homoclinic orbit Poincaré map Piecewise affine system 



This study was supported by Natural Science Foundation of China (No. 11671149) and Natural Science Foundation of Guangdong Province (No. 2017A030312006).


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© Springer Science+Business Media B.V., part of Springer Nature 2018

Authors and Affiliations

  1. 1.School of MathematicsSouth China University of TechnologyGuangzhouChina

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