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Abstract

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 newhyperchaos 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 selfsynchronization for the newhyperchaos 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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Authors and Affiliations

Sundarapandian Vaidyanathan
1
Shaobo He
2
Aceng Sambas
3

  1. School of Electrical and Computing, Vel Tech University, 400 Feet Outer Ring Road, Avadi, Chennai-600092, Tamil Nadu, India
  2. School of Physics and Electronics, Central South University, Changsha, 410083, China
  3. Department of Mechanical Engineering, Universitas Muhammadiyah Tasikmalaya, Tasikmalaya 46196, West Java, Indonesia
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Abstract

In this work, we present new results for a two-scroll 4-D hyperchaotic system with a unique saddle point equilibrium at the origin. The bifurcation and multi-stability analysis for the new hyperchaotic system are discussed in detail. As a control application, we develop a feedback control based on integral sliding mode control (ISMC) for the complete synchronization of a pair of two-scroll hyperchaotic systems developed in this work. Numerical simulations using Matlab are provided to illustrate the hyperchaotic phase portraits, bifurcation diagrams and synchronization results. Finally, as an electronic application, we simulate the new hyperchaotic system using Multisim for real-world implementations.
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Authors and Affiliations

Sundarapandian Vaidyanathan
1
Irene M. Moroz
2
Aceng Sambas
3 4

  1. Centre for Control Systems, Vel Tech University, 400 Feet Outer Ring Road, Avadi, Chennai-600092, Tamil Nadu, India
  2. Mathematical Institute, University of Oxford, Andrew Wiles Building, ROQ, Oxford Ox2 6GG, UK
  3. Faculty of Informatics and Computing, Universiti Sultan Zainal Abidin, Gong Badak, 21300, Terengganu, Malaysia
  4. Department of Mechanical Engineering, Universitas MuhammadiyahTasikmalaya, Tasikmalaya 46196,West Java, Indonesia
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Abstract

In this work, we modify the dynamics of 3-D four-wing Li chaotic system (Li et al. 2015) by introducing a feedback controller and obtain a new 4-D hyperchaotic four-wing system with complex properties. We show that the new hyperchaotic four-wing system have three saddle-foci balance points, which are unstable. We carry out a detailed bifurcation analysis for the new hyperchaotic four-wing system and show that the hyperchaotic four-wing system has multistability and coexisting attractors. Using integral sliding mode control, we derive new results for the master-slave synchronization of hyperchaotic four-wing systems. Finally, we design an electronic circuit using MultiSim for real implementation of the new hyperchaotic four-wing system.
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Authors and Affiliations

Sundarapandian Vaidyanathan
1
Khaled Benkouider
2
Aceng Sambas
3
Samy Abdelwahab Safaan
4 5

  1. School of Electrical and Computing, Vel Tech University, 400 Feet Outer Ring Road, Avadi, Chennai-600092, Tamil Nadu, India
  2. Non Destructive Testing Laboratory, Automatic Department, Jijel University, BP 98, 18000, Jijel, Algeria
  3. Department of Mechanical Engineering, Universitas Muhammadiyah Tasikmalaya, Tasikmalaya 46196, West Java, Indonesia
  4. Department of Natural and Applied Sciences, Community College of Buraydah, Qassim University, Buraydah, 52571, Saudi Arabia
  5. Nile Higher Institute for Commercial Science and Computer Technology, Mansoura, 35511, Egypt

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