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Nonlinear Dynamics

, Volume 95, Issue 1, pp 381–390 | Cite as

Hidden and self-excited coexisting attractors in a Lorenz-like system with two equilibrium points

  • Shijian CangEmail author
  • Yue Li
  • Ruiye Zhang
  • Zenghui Wang
Original Paper
  • 278 Downloads

Abstract

This paper reports the finding of unusual hidden and self-excited coexisting dynamical behaviors in an existing Lorenz-like system. For different parameters, the system has different types of equilibrium points, such as saddle-nodes, stable focus-nodes, saddle-foci and nonhyperbolic equilibrium points, which can be used to find different types of hidden and self-excited attractors. The different types of attractors have been vividly demonstrated by several numerical techniques including phase portraits, bifurcation diagrams and basins of attraction. Very interestingly, we find the rare coexistence of chaotic attractor and periodic orbits in the Lorenz-like system with two saddle-foci.

Keywords

Hidden attractors Coexisting attractors Lorenz-like system Bifurcation Basins of attraction 

Notes

Acknowledgements

We would like to thank the anonymous referees for their valuable suggestions and questions. This work is partly supported by the National Natural Science Foundation of China (Grant Nos. 61873186 and 61773282), the Application Base and Frontier Technology Research Project of Tianjin of China (Grant No. 13JCQNJC03600) and South African National Research Foundation (Grant Nos. 112142 and 112108), South African National Research Foundation Incentive Grant (No. 114911) and Tertiary Education Support Programme (TESP) of South African ESKOM.

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflicts of interest.

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Copyright information

© Springer Nature B.V. 2018

Authors and Affiliations

  1. 1.Department of Product DesignTianjin University of Science and TechnologyTianjinPeople’s Republic of China
  2. 2.School of Electronic Information and AutomationTianjin University of Science and TechnologyTianjinPeople’s Republic of China
  3. 3.School of Electrical and Information EngineeringTianjin UniversityTianjinPeople’s Republic of China
  4. 4.Department of Electrical and Mining EngineeringUniversity of South AfricaFloridaSouth Africa

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