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Number of results: 15
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Abstract

This paper announces an eight-term novel 3-D jerk chaotic system with three quadratic nonlinearities. The phase portraits of the novel jerk chaotic system are displayed and the qualitative properties of the jerk system are described. The novel jerk chaotic system has two equilibrium points, which are saddle-foci and unstable. The Lyapunov exponents of the novel jerk chaotic system are obtained as L1 = 0.20572,L2 = 0 and L3 = −1.20824. Since the sum of the Lyapunov exponents of the jerk chaotic system is negative, we conclude that the chaotic system is dissipative. The Kaplan-Yorke dimension of the novel jerk chaotic system is derived as DKY = 2.17026. Next, an adaptive controller is designed via backstepping control method to globally stabilize the novel jerk chaotic system with unknown parameters. Moreover, an adaptive controller is also designed via backstepping control method to achieve global chaos synchronization of the identical jerk chaotic systems with unknown parameters. The backstepping control method is a recursive procedure that links the choice of a Lyapunov function with the design of a controller and guarantees global asymptotic stability of strict feedback systems. MATLAB simulations have been depicted to illustrate the phase portraits of the novel jerk chaotic system and also the adaptive backstepping control results.
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Authors and Affiliations

Sundarapandian Vaidyanathan
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Abstract

This paper investigates the backstepping control design with novel feedback input ap-proach for controlling chaotic systems to guarantee the complete synchronization as well asthe anti-synchronization of chaotic systems, viz. n–scroll Chua (K. Wallace et.al. 2001) andLur’e chaotic systems. Our theorems on hybrid synchronization for n–scroll Chua and Lur’e(J.Suyken et.al. 1997) chaotic systems is established using Lyapunov stability theory. Based onthe Lyapunov function, the backstepping control is determined to tune the controller gain basedon the precalculated feedback control inputs. The backstepping scheme is recursive procedurethat links the choice of a Lyapunov function with the design of a controller and guaranteesglobal stability performance of strict-feedback chaotic systems. Since the Lyapunov exponentsare not required for these calculations, the backstepping control method is effective and conve-nient to synchronize the chaotic systems. Mainly this technique gives the flexibility to constructa control law. Numerical simulations are also given to illustrate and validate the hybrid synchro-nization results derived in this paper.
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Authors and Affiliations

Suresh Rasappan
Sundarapandian Vaidyanathan
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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

A new 4-D dynamical system exhibiting chaos is introduced in this work. The proposed nonlinear plant with chaos has an unstable rest point and a line of rest points. Thus, the new nonlinear plant exhibits hidden attractors. A detailed dynamic analysis of the new nonlinear plant using bifurcation diagrams is described. Synchronization result of the new nonlinear plant with itself is achieved using Integral Sliding Mode Control (ISMC). Finally, a circuit model using MultiSim of the new 4-D nonlinear plant with chaos is carried out for practical use.

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Authors and Affiliations

Sundarapandian Vaidyanathan
Aceng Sambas
Sen Zhang
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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

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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Authors and Affiliations

Sundarapandian Vaidyanathan
Irene M. Moroz
Aceng Sambas
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Abstract

In this work, we present results for a new dissipative jerk chaotic system with three quadratic terms in its dynamics.We describe the bifurcation analysis for the new jerk system and also show that the proposed system exhibits multi-stability. Next, we describe a backstepping control-based synchronization design for a pair of new jerk chaotic systems. MATLAB simulations are put forth to exhibit the various findings in this work. Furthermore, we exhibit a circuit simulation for the new jerk system using MultiSim.
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Authors and Affiliations

Sundarapandian Vaidyanathan
1
Khaled Benkouider
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. 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
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Abstract

In the recent years, chaotic systems with uncountable equilibrium points such as chaotic systems with line equilibrium and curve equilibrium have been studied well in the literature. This reports a new 3-D chaotic system with an axe-shaped curve of equilibrium points. Dynamics of the chaotic system with the axe-shaped equilibrium has been studied by using phase plots, bifurcation diagram, Lyapunov exponents and Lyapunov dimension. Furthermore, an electronic circuit implementation of the new chaotic system with axe-shaped equilibrium has been designed to check its feasibility. As a control application, we report results for the synchronization of the new system possessing an axe-shaped curve of equilibrium points.

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Authors and Affiliations

Sundarapandian Vaidyanathan
Aceng Sambas
Mustafa Mamat
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Abstract

In this work, we report a new chaotic population biology system with one prey and two predators. Our new chaotic population model is derived by introducing two nonlinear interaction terms between the prey and predator-2 to the Samardzija-Greller population biology system (1988).We show that the new chaotic population biology system has a greater value of Maximal Lyapunov Exponent (MLE) than the Maximal Lyapunov Exponent (MLE) of the Samardzija- Greller population biology system (1988).We carry out a detailed bifurcation analysis of the new chaotic population biology system with one prey and two predators. We also show that the new chaotic population biology model exhibits multistability with coexisting chaotic attractors. Next, we use the integral sliding mode control (ISMC) for the complete synchronization of the new chaotic population biology system with itself, taken as the master and slave chaotic population biology systems. Finally, for practical use of the new chaotic population biology system, we design an electronic circuit design using Multisim (Version 14.0).
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Authors and Affiliations

Sundarapandian Vaidyanathan
1
Khaled Benkouider
2
Aceng Sambas
3
P. Darwin
4

  1. Centre for Control Systems, 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 Computer Science and Engineering, Rajalakshmi Institute of Technology, Kuthambakkam, Chennai-600 124, Tamil Nadu, India
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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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Abstract

Abstract 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.
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Authors and Affiliations

Sundarapandian Vaidyanathan
Aceng Sambas
Mustafa Mamat
Mada Sanjaya Ws
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Abstract

Researchers have paid significant attention on hyperjerk systems, especial hyperjerk ones with chaos. A new hyperjerk system with seven terms and two parameters is analyzed. Chaotic attractors as well as coexisting attractors are displayed by the hyperjerk system. Thus it is a new multi-stable chaotic hyperjerk system. Further properties of the proposed hyperjerk system such as circuit design and backstepping-based control and synchronization are reported.

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Authors and Affiliations

Viet-Thanh Pham
Sundarapandian Vaidyanathan
Christos Volos
Sajad Jafari
Tomasz Kapitaniak
ORCID: ORCID
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Abstract

In this work, a new 3-D modified WINDMI chaotic jerk system with exponential and sinusoidal nonlinearities is presented and its dynamical behaviours and properties are investigated. Firstly, some properties of the system are studied such as equilibrium points and their stability, Lyapunov exponents and Kaplan-Yorke dimension. Also, we study the new jerk system dynamics using numerical simulations and analyses, including phase portraits, Lyapunouv exponent spectrum, bifurcation diagram and Poincaré map, 0-1 test. Next, we exhibit that the new 3-D chaotic modified WINDMI jerk system has multistability with coexisting chaotic attractors. Moreover, we design an electronic circuit using MultiSim 14.1 for real implementation of the modified WINDMI chaotic jerk system. Finally, we design an active synchronization scheme for the complete synchronization of the modified WINDMI chaotic jerk systems via backstepping control.
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Authors and Affiliations

Mohamad Afendee Mohamed
1
Sundarapandian Vaidyanathan
2 3
Fareh Hannachi
4
Aceng Sambas
1
P. Darwin
5

  1. Faculty of Information and Computing,Universiti Sultan Zainal Abidin, Terengganu, Malaysia
  2. Centre for ControlSystems, Vel Tech University, 400 Feet Outer Ring Road, Avadi, Chennai-600062 Tamil Nadu, India
  3. Faculty of Information and Computing, Universiti Sultan Zainal Abidin Terengganu, Malaysia
  4. Larbi Tebessi University – Tebessi routede constantine, 12022, Tebessa, Algeria
  5. Department of Computer Science and EngineeringRajalakshmi Institute of Technology, Kuthambakkam, Chennai-600 124, Tamil Nadu, India
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Abstract

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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Authors and Affiliations

Sundarapandian Vaidyanathan
Sajad Jafar
Viet-Thanh Pham
Ahmad Taher Azar
Fawaz E. Alsaadi

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