A New 4-D Multi-Stable Hyperchaotic Two-Scroll System with No-Equilibrium and its Hyperchaos Synchronization
S. Vaidyanathan1,*, C-H Lien2 , W. Fuadi3 , Mujiarto4 , M. Mamat5 and Subiyanto6

1 Research and Development Centre, Vel Tech University, Avadi, Chennai, India
2 Department of Marine Engineering, National Kaohsiung University of Science and Technology, Kaohsiung, 811, Taiwan, R.O.C.
3 Department of Informatic, Universitas Malikussaleh, Aceh Utara, Indonesia
4 Department of Mechanical Engineering, Universitas Muhammadiyah Tasikmalaya, Indonesia
5 Faculty of Informatics and Computing, Universiti Sultan Zainal Abidin, Kuala Terengganu, Malaysia
6 Department of Marine Science, Faculty of Fishery and Marine Science, Universitas Padjadjaran, Indonesia

Abstract

A new 4-D multi-stable hyperchaotic two-scroll system with four quadratic
nonlinearities is proposed in this paper. The dynamical properties of the new hyperchaotic
system are described in terms of finding equilibrium points, phase portraits, Lyapunov
exponents, Kaplan-Yorke dimension, dissipativity, etc. We discover that the new hyperchaotic
system has no equilibrium point and hence it exhibits a hidden attractor. Furthermore, we show
that the new hyperchaos system has multi-stability by the coexistence of hyperchaotic
attractors for different values of initial conditions. As a control application, we use integral
sliding mode control (ISMC) to derive new results for the hyperchaos synchronization of the
new 4-D multi-stable hyperchaotic two-scroll system with hidden attractor.

Keywords: 4-D multi-stable, hyperchaotic two-scroll system

Topic: Engineering and Technology