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Chin. Phys. B, 2018, Vol. 27(11): 110201    DOI: 10.1088/1674-1056/27/11/110201
Special Issue: SPECIAL TOPIC — 80th Anniversary of Northwestern Polytechnical University (NPU)
SPECIAL TOPIC—80th Anniversary of Northwestern Polytechnical University (NPU)   Next  

Heteroclinic cycles in a new class of four-dimensional discontinuous piecewise affine systems

Wenjing Xu(徐文静), Wei Xu(徐伟), Li Cai(蔡力)
School of Science, Northwestern Polytechnical University, Xi'an 710129, China
Abstract  

It is a huge challenge to give an existence theorem for heteroclinic cycles in the high-dimensional discontinuous piecewise systems (DPSs). This paper first provides a new class of four-dimensional (4D) two-zone discontinuous piecewise affine systems (DPASs), and then gives a useful criterion to ensure the existence of heteroclinic cycles in the systems by rigorous mathematical analysis. To illustrate the feasibility and efficiency of the theory, two numerical examples, exhibiting chaotic behaviors in a small neighborhood of heteroclinic cycles, are discussed.

Keywords:  heteroclinic cycle      chaos      discontinuous piecewise affine system  
Received:  20 June 2018      Revised:  05 September 2018      Published:  05 November 2018
PACS:  02.60.-x (Numerical approximation and analysis)  
  05.45.-a (Nonlinear dynamics and chaos)  
Fund: 

Project supported by the National Natural Science Foundation of China (Grant Nos. 11472212 and 11532011).

Corresponding Authors:  Wei Xu     E-mail:  weixu@nwpu.edu.cn

Cite this article: 

Wenjing Xu(徐文静), Wei Xu(徐伟), Li Cai(蔡力) Heteroclinic cycles in a new class of four-dimensional discontinuous piecewise affine systems 2018 Chin. Phys. B 27 110201

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