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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

The purpose of this paper is to introduce a new chaotic oscillator. Although different chaotic systems have been formulated by earlier researchers, only a few chaotic systems exhibit chaotic behaviour. In this work, a new chaotic system with chaotic attractor is introduced. It is worth noting that this striking phenomenon rarely occurs in respect of chaotic systems. The system proposed in this paper has been realized with numerical simulation. The results emanating from the numerical simulation indicate the feasibility of the proposed chaotic system. More over, chaos control, stability, diffusion and synchronization of such a system have been dealt with.
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Bibliography

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Authors and Affiliations

Suresh Rasappan
1
K.A. Niranjan Kumar
1

  1. Department of Mathematics, Vel Tech Rangarajan Dr.Sagunthala R&D Institute of Science and Technology, Avadi, Chennai-62, India
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Abstract

The Bulletin of the Polish Academy of Sciences: Technical Sciences (Bull.Pol. Ac.: Tech.) is published bimonthly by the Division IV Engineering Sciences of the Polish Academy of Sciences, since the beginning of the existence of the PAS in 1952. The journal is peer‐reviewed and is published both in printed and electronic form. It is established for the publication of original high quality papers from multidisciplinary Engineering sciences with the following topics preferred: Artificial and Computational Intelligence, Biomedical Engineering and Biotechnology, Civil Engineering, Control, Informatics and Robotics, Electronics, Telecommunication and Optoelectronics, Mechanical and Aeronautical Engineering, Thermodynamics, Material Science and Nanotechnology, Power Systems and Power Electronics.

Journal Metrics: JCR Impact Factor 2018: 1.361, 5 Year Impact Factor: 1.323, SCImago Journal Rank (SJR) 2017: 0.319, Source Normalized Impact per Paper (SNIP) 2017: 1.005, CiteScore 2017: 1.27, The Polish Ministry of Science and Higher Education 2017: 25 points.

Abbreviations/Acronym: Journal citation: Bull. Pol. Ac.: Tech., ISO: Bull. Pol. Acad. Sci.-Tech. Sci., JCR Abbrev: B POL ACAD SCI-TECH Acronym in the Editorial System: BPASTS.

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Authors and Affiliations

Sanjay Kumar
Chaman Singh
Sada Nand Prasad
Chandra Shekhar
Rajiv Aggrawal
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Abstract

The purpose of this paper is to introduce a new chaotic oscillator. Although different chaotic systems have been formulated by earlier researchers, only a few chaotic systems exhibit chaotic behaviour. In this work, a new chaotic system with chaotic attractor is introduced for triangular wave non-linearity. It is worth noting that this striking phenomenon rarely occurs in respect of chaotic systems. The system proposed in this paper has been realized with numerical simulation. The results emanating from the numerical simulation indicate the feasibility of the proposed chaotic system. More over, chaos control, stability, diffusion and synchronization of such a system have been dealt with.
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Authors and Affiliations

Rasappan Suresh
1
Kumaravel Sathish Kumar
2
Murugesan Regan
2
K.A. Niranjan Kumar
2
R. Narmada Devi
2
Ahmed J. Obaid
3

  1. Mathematics Section, Department of Information Technology, College of Computing and Information Sciences, University of Technology and Applied Sciences, Ibri, Sultanate of Oman
  2. Department of Mathematics, Vel Tech Rangarajan Dr.Sagunthala R& D Institute of Science and Technology, Avadi, Chennai-62, India
  3. Faculty of Computer Science and Mathematics, University of Kufa, Iraq
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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

Shaft-stator rub and cracks on rotors, which have devastating effects on the industrial equipment, cause nonlinear and in some cases chaotic lateral vibrations. On the other hand, vibrations caused by machinery faults can be torsional in cases such as rub. Therefore, a combined analysis of lateral and torsional vibrations and extraction of chaotic features from these vibrations is an effective approach for rotor vibration monitoring. In this study, lateral and torsional vibrations of rotors have been examined for detecting cracks and rub. For this purpose, by preparing a laboratory model, the lateral vibrations of a system with crack and rub have been acquired. After that, a practical method for measuring the torsional vibrations of the system is introduced. By designing and installing this measurement system, practical test data were acquired on the laboratory setup. Then, the method of phase space reconstruction was used to examine the effect of faults on the chaotic behaviour of the system. In order to diagnose the faults based on the chaotic behaviour of the system, largest Lyapunov exponent (LLE), approximate entropy (ApEn) and correlation dimension were calculated for a healthy system and also for a system with rub and a crack. Finally, by applying these parameters, the chaotic feature space is introduced in order to diagnose the intentionally created faults. The results show that in this space, the distinction between the various defects in the system can be clearly identified, which enables to use this method in fault diagnosis of rotating machinery.

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Authors and Affiliations

Ali Hajnayeb
Kourosh Heidari Shirazi
Reza Aghaamiri

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