Regular Article

Constructing hyperchaotic attractors of conditional symmetry

¹ Jiangsu Collaborative Innovation Center of Atmospheric Environment and Equipment Technology (CICAEET), Nanjing University of Information Science & Technology, Nanjing 210044, P.R. China
² Jiangsu Key Laboratory of Meteorological Observation and Information Processing, Nanjing University of Information Science & Technology, Nanjing 210044, P.R. China
³ School of Electrical, Electronic, and Computing Engineering, The University of Western Australian, 35 Stirling Highway, Crawley, WA 6009, Australia
⁴ School of Electrical and Automation Engineering, Nanjing Normal University, Nanjing 210042, P.R. China

^a e-mail: chunbiaolee@nuist.edu.cn

Received: 27 March 2019
Received in final form: 30 March 2019
Published online: 2 October 2019

Abstract

By applying the symmetry property of nonlinear function for obtaining new polarity balance, hyperchaotic systems of conditional symmetry are constructed, and coexisting hyperchaotic attractors of conditional symmetry originated from 1-D and 2-D offset boosting are captured accordingly. More interestingly, a symmetric hyperchaotic system is proven to host conditional symmetry, and consequently output coexisting symmetric pair of attractors and their duplication of conditional symmetry. Consequently, two independent processes of attractor merging are observed, which have not been previously reported. Furthermore, the property of offset boosting is discussed for the newly constructed hyperchaotic systems. Circuit implementation based on the develop kit of STM32 is developed, it demonstrates those coexisting attractors are in good agreement with the theoretical analysis and numerical simulations.