Title: Analysis, synchronisation and circuit implementation of a novel jerk chaotic system and its application for voice encryption

Authors: Sundarapandian Vaidyanathan; Aceng Sambas; Mustafa Mamat; Mada Sanjaya WS

Addresses: Research and Development Centre, Vel Tech University, Avadi, Chennai-600 062, Tamil Nadu, India ' Department of Mechanical Engineering, Universitas Muhammadiyah Tasikmalaya, Indonesia ' Faculty of Informatics and Computing, Universiti Sultan Zainal Abidin, Juala Terengganu, Malaysia ' Department of Physics, Universitas Islam Negeri Sunan Gunung Djati Bandung, Indonesia

Abstract: In this research work, a novel 3D jerk chaotic system with one-quadratic nonlinearity and two-cubic nonlinearities is designed to generate complex chaotic signals. We show that the novel jerk chaotic system has a unique equilibrium at the origin, which is a saddle-focus and unstable. The Lyapunov exponents of the novel jerk chaotic system are obtained as L₁ = 0.30899, L₂ = 0 and L₃ = -4.11304. The Kaplan-Yorke dimension of the novel jerk chaotic system is obtained as D_KY = 2.0751. The qualitative properties of the novel jerk chaotic system are described in detail and MATLAB plots are shown. Next, we use backstepping control method to establish global chaos synchronisation of the identical novel jerk chaotic systems with unknown parameters. Next, an electronic circuit realisation of the novel jerk chaotic system is presented using MultiSIM to confirm the feasibility of the theoretical model. Finally, we present an application of the novel jerk chaotic system for voice encryption. The comparison between the MATLAB 2010 and MultiSIM 10.0 simulation results demonstrate the effectiveness of the proposed voice encryption scheme.

Keywords: chaos; chaotic systems; jerk systems; Lyapunov exponents; chaos synchronisation; backstepping control; circuit implementation; voice encryption.

DOI: 10.1504/IJMIC.2017.085934

International Journal of Modelling, Identification and Control, 2017 Vol.28 No.2, pp.153 - 166

Received: 22 Jul 2016
Accepted: 12 Sep 2016
Published online: 18 Aug 2017 *

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