Title: A generalised incomplete no-equilibria transformation method to construct a hidden multi-scroll system with no-equilibrium

Authors: Lihong Tang; Zongmei He; Yanli Yao; Ce Yang

Addresses: Changsha Social Work College, Changsha, China ' School of Software, Changsha Social Work College, Changsha, China ' School of Aeronautical Engineering, Binzhou University, Binzhou, China ' School of Computer Science and Engineering, Hunan University of Science and Technology, Xiangtan, China; Hunan Key Laboratory for Service Computing and Novel Software Technology, Xiangtan, China

Abstract: At present, there is a lot of research on multi-scroll chaotic systems with equilibrium points. However, there are few studies on no-equilibrium multi-scroll chaotic systems. This paper proposes a generalised incomplete no-equilibrium transformation method to design no-equilibrium multi-scroll chaotic systems. Firstly, a no-equilibrium chaotic system is constructed by adopting the proposed method. Phase plots and Lyapunov exponents show that the constructed no-equilibrium chaotic system can generate hidden hyperchaotic attractors. Then, a no-equilibrium multi-scroll hyperchaotic system is realised by introducing multi-level logic pulse signals. Theoretical analysis and numerical simulation show that the designed no-equilibrium multi-scroll hyperchaotic system can generate hidden multidirectional multi-double-scroll attractors including 1D, 2D, and 3D hidden multi-scroll hyperchaotic attractors. Finally, an analogue circuit of the no-equilibrium multi-scroll hyperchaotic system is implemented by using commercial electronic elements. Various typical hidden multi-scroll attractors are verified on MULTISIM platform.

Keywords: no-equilibrium; hidden attractors; multi-scroll; multi-level pulse.

DOI: 10.1504/IJCSE.2024.136251

International Journal of Computational Science and Engineering, 2024 Vol.27 No.1, pp.57 - 67

Received: 15 Jul 2022
Received in revised form: 03 Aug 2022
Accepted: 10 Aug 2022
Published online: 25 Jan 2024 *

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