https://doi.org/10.1140/epjst/e2015-02481-0
Regular Article
A 5-D hyperchaotic Rikitake dynamo system with hidden attractors
1 Vel Tech University, Research and Development Centre, Avadi, Chennai-600 062, Tamil Nadu, India
2 School of Electronics and Telecommunications, Hanoi University of Science and Technology, 01 Dai Co Viet, Hanoi, Vietnam
3 Physics Department, Aristotle University of Thessaloniki, 54124 Thessaloniki, Greece
a e-mail: sundarvtu@gmail.com
Received: 8 March 2015
Revised: 20 May 2015
Published online: 27 July 2015
This paper presents a 5-D hyperchaotic Rikitake dynamo system with three positive Lyapunov exponents which is derived by adding two state feedback controls to the famous 3-D Rikitake two-disk dynamo system. It is noted that the proposed hyperchaotic system has no equilibrium points and hence it exhibits hidden attractors. In addition, the qualitative properties, as well as the adaptive synchronization of the hyperchaotic Rikitake dynamo system with unknown system parameters, are discussed in details. The main results are proved using Lyapunov stability theory and numerical simulations are shown using MATLAB. Moreover, an electronic circuit realization in SPICE has been detailed to confirm the feasibility of the theoretical 5-D hyperchaotic Rikitake dynamo model.
© EDP Sciences, Springer-Verlag, 2015
