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Analysis, synchronisation and circuit design of a new highly nonlinear chaotic system. (English) Zbl 1385.93037
Summary: This paper investigates a three-dimensional autonomous chaotic flow without linear terms. Dynamical behavior of the proposed system is investigated through eigenvalue structures, phase portraits, bifurcation diagram, Lyapunov exponents and basin of attraction. For a suitable choice of the parameters, the proposed system can exhibit anti-monotonicity, periodic oscillations and double-scroll chaotic attractor. Basin of attraction of the proposed system shows that the chaotic attractor is self-excited. Furthermore, feasibility of double-scroll chaotic attractor in the real word is investigated by using the OrCAD-PSpice software via an electronic implementation of the proposed system. A good qualitative agreement is illustrated between the numerical simulations and the OrCAD-PSpice results. Finally, a finite-time control method based on dynamic sliding surface for the synchronization of master and slave chaotic systems in the presence of external disturbances is performed. Using the suggested control technique, the superior master-slave synchronization is attained. Illustrative simulation results on the studied chaotic system are presented to indicate the effectiveness of the suggested scheme.

MSC:
93C15 Control/observation systems governed by ordinary differential equations
34H10 Chaos control for problems involving ordinary differential equations
93C10 Nonlinear systems in control theory
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