Synchronisation, electronic circuit implementation, and fractional-order analysis of 5D ordinary differential equations with hidden hyperchaotic attractors

Pramana: Journal of physics

WEI ZHANG^4¹  SIFEU TAKOUGANG KINGNI^5²  AKIF AKGÜL^6⁴  KARTHIKEYAN RAJAGOPAL^3⁵  ZHOUCHAO WEI^1,2⁶ 

[1] Center for Nonlinear Dynamics, Department of Electrical and Communication Engineering, The PNG University of Technology, Lae, Papua New Guinea^3;College of Mechanical Engineering, Beijing University of Technology, Beijing 100124, China^4;Department of Electrical and Electronics Engineering, Faculty of Technology, Sakarya University, Adapazarı, Sakarya, Turkey^6;Department of Mechanical and Electrical Engineering, Institute of Mines and Petroleum Industries, University of Maroua, P.O. Box 46, Maroua, Cameroon^5;Guangxi Colleges and Universities Key Laboratory of Complex System Optimization and Big Data Processing, Yulin Normal University, Yulin 537000, China^2;School of Mathematics and Physics, China University of Geosciences, Wuhan 430074, China^1

关键词: Hyperchaos;    hidden attractor;    synchronisation;    circuit implementation;    fractional-order analysis;   

DOI  :  

学科分类：物理（综合）

来源: Indian Academy of Sciences

【 摘 要 】

Hidden hyperchaotic attractors can be generated with three positive Lyapunov exponents in the proposed 5D hyperchaotic Burke–Shaw system with only one stable equilibrium. To the best of our knowledge, this feature has rarely been previously reported in any other higher-dimensional systems. Unidirectional linear error feedback coupling scheme is used to achieve hyperchaos synchronisation, which will be estimated by using two indicators: the normalised average root-mean squared synchronisation error and the maximum cross-correlation coefficient. The 5D hyperchaotic system has been simulated using a specially designed electronic circuit and viewed on an oscilloscope, thereby confirming the results of the numerical integration. In addition, fractional-order hidden hyperchaotic system will be considered from the following three aspects: stability, bifurcation analysis and FPGA implementation. Such implementations in real time represent hidden hyperchaotic attractors with important consequences for engineering applications.

【 授权许可】

CC BY