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Chin. Phys. B, 2017, Vol. 26(8): 080201    DOI: 10.1088/1674-1056/26/8/080201
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Coexisting hidden attractors in a 4D segmented disc dynamo with one stable equilibrium or a line equilibrium

Jianghong Bao(鲍江宏), Dandan Chen(陈丹丹)
School of Mathematics, South China University of Technology, Guangzhou 510641, China
Abstract  

This paper introduces a four-dimensional (4D) segmented disc dynamo which possesses coexisting hidden attractors with one stable equilibrium or a line equilibrium when parameters vary. In addition, by choosing an appropriate bifurcation parameter, the paper proves that Hopf bifurcation and pitchfork bifurcation occur in the system. The ultimate bound is also estimated. Some numerical investigations are also exploited to demonstrate and visualize the corresponding theoretical results.

Keywords:  coexisting hidden attractors      4D segmented disc dynamo      pitchfork bifurcation      Hopf bifurcation      ultimate bound estimation  
Received:  23 February 2017      Revised:  16 April 2017      Published:  05 August 2017
PACS:  02.30.Hq (Ordinary differential equations)  
  02.30.Oz (Bifurcation theory)  
  05.45.-a (Nonlinear dynamics and chaos)  
Fund: 

Project supported by the National Natural Science Foundation of China (Grant No. 11671149).

Corresponding Authors:  Jianghong Bao     E-mail:  majhbao@yahoo.com
About author:  0.1088/1674-1056/26/8/

Cite this article: 

Jianghong Bao(鲍江宏), Dandan Chen(陈丹丹) Coexisting hidden attractors in a 4D segmented disc dynamo with one stable equilibrium or a line equilibrium 2017 Chin. Phys. B 26 080201

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