Synchronisation, electronic circuit implementation, and fractional-order analysis of 5D ordinary differential equations with hidden hyperchaotic attractors
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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.
KeywordsHyperchaos hidden attractor synchronisation circuit implementation fractional-order analysis
PACS Nos02.30.Oz 02.30.Hq
This work was supported by the Natural Science Foundation of China (Nos 11772306 and 11401543), the Open Foundation for Guangxi Colleges and Universities Key Lab of Complex System Optimization and Big Data Processing (No. 2016CSOBDP0202), Scientific Research Program of Hubei Provincial Department of Education (No. B2017599), the Fundamental Research Funds for the Central Universities, China University of Geosciences (Wuhan) (No. CUGL150419) and Sakarya University Scientific Research Projects Unit (No. 201609-00-008).
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