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A new multistable double-scroll 4-D hyperchaotic system with no equilibrium point, its bifurcation analysis, synchronization and circuit design

Vaidyanathan Sundarapandian, He Shaobo, Simbas Aceng

Archives of Control Sciences

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2021

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Vol. 31, No. 1

99--128

EN

In this work, we have developed a new 4-D dynamical system with hyperchaos and hidden attractor. First, by introducing a feedback input control into the 3-D Ma chaos system (2004), we obtain a new 4-D hyperchaos system with no equilibrium point. Thus, we derive a new hyperchaos system with hidden attractor. We carry out an extensive bifurcation analysis of the new hyperchaos model with respect to the three parameters. We also carry out probability density distribution analysis of the new hyperchaotic system. Interestingly, the new nonlinear hyperchaos system exhibits multistability with coexisting attractors. Next, we discuss global hyperchaos self-synchronization for the new hyperchaos system via Integral Sliding Mode Control (ISMC). As an engineering application, we realize the new 4-D hyperchaos system with an electronic circuit via MultiSim. The outputs of the MultiSim hyperchaos circuit show good match with the numerical MATLAB plots of the hyperchaos model. We also analyze the power spectral density (PSD) of the hyperchaos of the state variables using MultiSim.

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A new 4-D hyperchaotic system with no equilibrium, its multistability, offset boosting and circuit simulation

Vaidyanathan Sundarapandian, Moroz Irene M., Sambas Aceng

Archives of Control Sciences

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2020

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Vol. 30, No. 3

575--597

EN

A new 4-D dynamical system with hyperchaos is reported in this work. It is shown that the proposed nonlinear dynamical system with hyperchaos has no equilibrium point. Hence, the new dynamical system exhibits hidden hyperchaotic attractor. An in-depth dynamic analysis of the new hyperchaotic system is carried out with bifurcation transition diagrams, multistability analysis, period-doubling bubbles and offset boosting analysis. Using Integral Sliding Mode Control (ISMC), global hyperchaos synchronization results of the new hyperchaotic system are described in detail. Furthermore, an electronic circuit realization of the new hyperchaotic system has been simulated in MultiSim software version 13.0 and the results of which are in good agreement with the numerical simulations using MATLAB.

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A 4-D chaotic hyperjerk system with a hidden attractor, adaptive backstepping control and circuit design

Vaidyanathan S., Jafari S., Pham V.-T., Azar A. T., Alsaadi F. E.

Archives of Control Sciences

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2018

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Vol. 28, No. 2

239--254

EN

A novel 4-D chaotic hyperjerk system with four quadratic nonlinearities is presented in this work. It is interesting that the hyperjerk system has no equilibrium. A chaotic attractor is said to be a hidden attractor when its basin of attraction has no intersection with small neighborhoods of equilibrium points of the system. Thus, our new non-equilibrium hyperjerk system possesses a hidden attractor. Chaos in the system has been observed in phase portraits and verified by positive Lyapunov exponents. Adaptive backstepping controller is designed for the global chaos control of the non-equilibrium hyperjerk system with a hidden attractor. An electronic circuit for realizing the non-equilibrium hyperjerk system is also introduced, which validates the theoretical chaotic model of the hyperjerk system with a hidden chaotic attractor.

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A new three-dimensional chaotic system with a hidden attractor, circuit design and application in wireless mobile robot

Vaidyanathan S., Sambas A., Mamat M., Sanjaya M.

Archives of Control Sciences

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2017

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Vol. 27, no. 4

541--554

EN

This research work proposes a new three-dimensional chaotic system with a hidden attractor. The proposed chaotic system consists of only two quadratic nonlinearities and the system possesses no critical points. The phase portraits and basic qualitative properties of the new chaotic system such as Lyapunov exponents and Lyapunov dimension have been described in detail. Finally, we give some engineering applications of the new chaotic system like circuit simulation and control of wireless mobile robot.