Abstract
Objective: To investigate a novel chaotic system with unique features, its synchronization using nonlinear active control, analog circuit design and application to secure communication. Methods/Analysis: Dynamical tools such as dissipative analysis, instability of equilibrium points, sensitivity to initial conditions, 0-1 test, recurrence plot, Poincare map, Lyapunov exponents, Lyapunov dimension, frequency spectrum and basin of attraction. Synchronization is achieved using modified nonlinear active control technique and analog circuit design, implementation is done in NI Multisim platform. MATLAB and Multisim results are presented to meet the adequate verification of theoretical approach. Findings: A three-dimensional chaotic system with only two nonlinear terms, three parameters and a total of eight terms are proposed. The proposed system has three saddle focus type equilibria. The proposed system is topologically different from Lorenz’s and Rossler’s, Lu’s, Chen’s, and Liu’s families. Such dynamic systems are very few in the literature as per authors best knowledge. The system has basin of chaotic attractors for which first Lyapunov exponent ranges between 2.5 to 3. Frequency spectrum and large positive Lyapunov exponent result comparatively large bandwidth of the proposed systems against some well-known chaotic systems. Chaos, periodic and stable behaviors are obtained by altering the system parameters. Novelty/Application: The proposed three-dimensional chaotic system has significant chaotic behavior and broader spectrum than the six chaotic systems like Lorenz, Rossler, Lu, Chen, BG and Liu systems. Unlike the conventional active control approach, the proposed nonlinear active control does not result decoupled error dynamics. The system has significantly large bandwidth which is helpful in the masking of message signals and enhances the security of transmitted signals during communication. Keywords: Analog circuit design; Chaos; Chaotic system; Chaosbased communication; Chaos synchronization; Nonlinear active control
Highlights
Past three decades, chaotic phenomena, synchronization, and control of chaos behavior have been found and investigated in engineering and technology
Several novel chaotic systems have been reported and designed to date, given the first three-dimensional (3D) autonomous chaotic system reported by Lorenz [7], such as Rossler system [8], Chen system [9], Chua system [10], Liu system [11], Lu system [12], other novel chaotic systems [13,14,15,16,17,18,19,20,21], etc
Synchronization between proposed chaotic system and its application to secure communication explored using a novel nonlinear active control followed by analog circuit design and simulation in NI Multisim platform
Summary
Chaotic phenomena, synchronization, and control of chaos behavior have been found and investigated in engineering and technology. The major issues are identified as [1] there is a need to develop a novel chaotic system with higher positive LE and broader bandwidth and [2] A improved nonlinear control technique is required which does not result unlike, trivial, decoupled error dynamics. 2. To design a nonlinear active control technique which results coupled error dynamics for the synchronization of chaotic systems and its application. Synchronization between proposed chaotic system and its application to secure communication explored using a novel nonlinear active control followed by analog circuit design and simulation in NI Multisim platform.
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