Title: Analysis, properties and control of an eight-term 3-D chaotic system with an exponential nonlinearity

Authors: Sundarapandian Vaidyanathan

Addresses: Research and Development Centre, Vel Tech University, Avadi, Chennai-600 062, Tamil Nadu, India

Abstract: In this research work, an eight-term 3-D novel chaotic system with an exponential nonlinearity has been derived. The basic qualitative properties of the 3-D chaotic system have been discussed in detail. The new chaotic system has only one equilibrium point, which is a saddle-point. Hence, the system has an unstable equilibrium. The Lyapunov exponents of the 3-D chaotic system are obtained as L₁ = 14.0893, L₂ = 0 and L₃ = -33.9828. Since the maximal Lyapunov exponent of the novel chaotic system is L₁ = 14.0893, which is a large value, the novel chaotic system has strong chaotic behaviour. The Lyapunov dimension of the chaotic system is obtained as D_L = 2.4146. Next, an adaptive control law has been designed to stabilise the unstable chaotic system with unknown system parameters. The adaptive control result has been established using Lyapunov stability theory. MATLAB simulations have been shown in detail to illustrate the phase portraits and adaptive control results for the novel chaotic system.

Keywords: chaos; chaotic systems; Lyapunov dimension; adaptive control; Lyapunov stability theory; Lyapunov exponents; exponential nonlinearity; simulation.

DOI: 10.1504/IJMIC.2015.068871

International Journal of Modelling, Identification and Control, 2015 Vol.23 No.2, pp.164 - 172

Received: 28 Jan 2014
Accepted: 08 Sep 2014
Published online: 16 Apr 2015 *

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