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Chaos in a simple snap system with only one nonlinearity, its adaptive control and real circuit design

Treść / Zawartość
Identyfikatory
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We study an elegant snap system with only one nonlinear term, which is a quadratic nonlinearity. The snap system displays chaotic attractors, which are controlled easily by changing a system parameter. By using analysis, simulations and a real circuit, the dynamics of such a snap system has been investigated. We also investigate backstepping based adaptive control schemes for the new snap system with unknown parameters.
Rocznik
Strony
73--96
Opis fizyczny
Bibliogr. 60 poz., rys., wykr., wzory
Twórcy
  • Nonlinear Systems and Applications, Faculty of Electrical & ElectronicsEngineering, Ton Duc Thang University, Ho Chi Minh City, Vietnam
  • Research and Development Centre, Vel Tech University, Avadi, Chennai-600062, Tamil Nadu, India
  • Department of Physics, Aristotle University of Thessaloniki, Thessaloniki, GR-54124, Greece
autor
  • Biomedical Engineering Department, Amirkabir University of Technology, Tehran 15875-4413, Iran
  • Department of Information Technology, Faculty of Computing and IT, King Abdulaziz University, Jeddah 21589
  • Department of Electrical and Computer Engineering, Faculty of Engineering, King Abdulaziz University, Jeddah 21589
Bibliografia
  • [1] S. Vaidyanathan and C. Volos: Advances and Applications in Chaotic Systems, Springer, Berlin, Germany, 2016.
  • [2] V. T. Pham, S. Vaidyanathan, C. Volos, and T. Kapitaniak: Nonlinear Dynamical Systems with Self-Excited and Hidden Attractors, Springer, Berlin, Germany, 2018.
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  • [6] K. Boualleague: A new class of neural networks and its applications, Neurocomputing, 249 (2017), 28–47.
  • [7] S. Vaidyanathan: Synchronization of 3-cells cellular neural network (CNN) attractors via adaptive control method, International Journal of PharmTech Research, 8(5) (2015), 946–955.
  • [8] S. Vaidyanathan, A. Sambas, M. Mamat, and M. Sanjaya Ws: A new three-dimensional chaotic system with a hidden attractor, circuit design and application in wireless mobile robot, Archives of Control Sciences, 27(4) (2017), 541–554.
  • [9] A. Sambas, S. Vaidyanathan, M. Mamat, W. S. M. Sanjaya, and D.S. Rahayu: A 3-D novel jerk chaotic system and its application in secure communication system and mobile robot navigation, Studies in Computational Intelligence, 636 (2016), 283–310.
  • [10] S. Vaidyanathan: Global chaos synchronization of the forced Van der Pol chaotic oscillators via adaptive control method, International Journal of PharmTech Research, 8(6) (2015), 156–166.
  • [11] S. Vaidyanathan and S. Rasappan: Hybrid synchronization of hyperchaotic Qi and Lü systems by nonlinear control, Communications in Computer and Information Science, 131 (2011), 585–593.
  • [12] S. Vaidyanathan: Hyperchaos, qualitative analysis, control and synchronisation of a ten-term 4-D hyperchaotic systemwith an exponential nonlinearity and three quadratic nonlinearities, International Journal of Modelling, Identification and Control, 23(4) (2015), 380–392.
  • [13] S. Vaidyanathan: Adaptive controller and synchronizer design for the Qi-Chen chaotic system, Lecture Notes of the Institute for Computer Sciences, Social-Informatics and Telecommunications Engineering, 85 (2012), 124–133.
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  • [15] S. Vaidyanathan, A. Sambas, M. Mamat, and M. Sanjaya Ws: Analysis, synchronisation and circuit implementation of a novel jerk chaotic system and its application for voice encryption, International Journal of Modelling, Identification and Control, 28(2) (2017), 153–166.
  • [16] S. Vaidyanathan and K. Rajagopal: LabVIEWimplementation of chaotic masking with adaptively synchronised forced Van der Pol oscillators and its application in real-time image encryption, International Journal of Simulation and Process Modelling, 12(2) (2017), 165–178.
  • [17] A. Akgul, I. Moroz, I. Pehlivan, and S. Vaidyanathan: A new four-scroll chaotic attractor and its engineering applications, Optik, 127(13) (2016), 5491–5499.
  • [18] S. Rasappan and S. Vaidyanathan: Global chaos synchronization of WINDMI and Coullet chaotic systems by backstepping control, Far East Journal of Mathematical Sciences, 67(2) (2012), 265–287.
  • [19] S. Vaidyanathan, C. K. Volos, K. Rajagopal, I. M. Kyprianidis, and I. N. Stouboulos: Adaptive backstepping controller design for the antisynchronization of identical WINDMI chaotic systems with unknown parameters and SPICE implementation, Journal of Engineering Science and Technology Review, 8(2) (2015), 74–82.
  • [20] S. Vaidyanathan: Adaptive control of the FitzHugh-Nagumo chaotic neuron model, International Journal of PharmTech Research, 8(6) (2015), 117–127.
  • [21] S. Vaidyanathan, A. Sambas, and M. Mamat: A new chaotic system with axe-shaped equilibrium, its circuit implementation and adaptive synchronization, Archives of Control Sciences, 28(3) (2018), 443–462.
  • [22] S. Vaidyanathan, O. A. Abba, G. Betchewe, and M. Alidou: A new three-dimensional chaotic system: Its adaptive control and circuit design, International Journal of Automation and Control, 13(1) (2019), 101–121.
  • [23] P. Daltzis, S. Vaidyanathan, V. T. Pham, C. Volos, E. Nistazakis, and G. Tombras: Hyperchaotic attractor in a novel hyperjerk system with two nonlinearities, Circuits, Systems, and Signal Processing, 37(2) (2018), 613–635.
  • [24] S. Vaidyanathan and C. Volos: Advances in Memristors, Memristive Devices and Systems, Springer, Berlin, Germany, 2017.
  • [25] O. I. Tacha, C. K. Volos, I. M. Kyprianidis, I. N. Stouboulos, S. Vaidyanathan, and V. T. Pham: Analysis, adaptive control and circuit simulation of a novel nonlinear finance system,AppliedMathematics and Computation, 276 (2016), 200–217.
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  • [27] S. Vaidyanathan: Analysis, control, and synchronization of a 3-D novel jerk chaotic system with two quadratic nonlinearities, Kyungpook Mathematical Journal, 55(3) (2015), 563–586.
  • [28] J. Kengne, Z. T. Njitacke, and H. Fotsin: Dynamical analysis of a simple autonomous jerk system with multiple attractors, Nonlinear Dynamics, 83 (2016), 751–765.
  • [29] C. Liu, J. Yi, X. Xi, L. An, and Y. Fu: Research on the multi-scroll chaos generation based on Jerk mode, Procedia Engineering, 29 (2012), 957–961.
  • [30] P. Loudopop, M. Kountchou, H. Fotsin, and S. Bowong: Practical finitetime synchronization of jerk systems: theory and experiment, Nonlinear Dynamics, 78 (2014), 597–607.
  • [31] B. Munmuangsaen, B. Srisuchinwong, and J. C. Sprott: Generalization of the simplest autonomous chaotic system, Physics Letters A, 375 (2011), 1445–1450.
  • [32] J. C. Sprott: A new chaotic jerk circuit, IEEE Transactions on Circuits and Systems-II: Express Briefs, 58 (2011), 240–243.
  • [33] K. H. Sun and J. C. Sprott: A simple jerk systemwith piecewise exponential nonlinearity, International Journal of Nonlinear Science and Numerical Simulation, 10 (2009), 1443–1450.
  • [34] S. Vaidyanathan: A new 3-D jerk chaotic system with two cubic nonlinearities and its adaptive backstepping control, Archives of Control Sciences, 27(3) (2017), 409–439.
  • [35] J. C. Sprott: Elegant Chaos, World Scientific, Singapore, 2010.
  • [36] K. E. Chlouverakis and J. C. Sprott: Chaotic hyperjerk systems, Chaos, Solitons & Fractals, 28 (2006), 739–746.
  • [37] F. Y. Dalkiran and J. C. Sprott: Simple chaotic hyperjerk system, International Journal of Bifurcation and Chaos, 26 (2026), 1650189.
  • [38] B. Munmuangsaen and B. Srisuchinwong: Elementary chaotic snap flows, Chaos, Solitons & Fractals, 44 (2011), 995–1003.
  • [39] B. Bao, X. Zou, Z. Liu, and F. Hu: Simple chaotic hyperjerk system, International Journal of Bifurcation and Chaos, 23 (2013), 1350135.
  • [40] M. F. Khan, F. Baig, and S. Beg: Steganography between silence intervals of audio in video content using chaotic map, Circuits Syst. Signal Process, 33 (2014), 3901–3919.
  • [41] E. Fatemi-Behbahani, K. Ansari-Asl, and E. Farshidi: A new approach to analysis and design of chaos-based random number generators using algorithmic converter, Circuits Syst. Signal Process, 35 (2016), 3830–3846.
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  • [43] J. F. Chang, T. L. Liao, J. J. Yan, and H. C. Chen: Implementation of synchronized chaotic Lu systems and its application in secure communication using PSO-based PI controller, Circuits Syst. Signal Process, 29 (2010), 527–538.
  • [44] F. C. M. Lau and G. Kolumban: Performance limit of chaotic digital wave form communication systems: Approach of maximizing a posteriori probability, Circuits Syst. Signal Process, 24 (2005), 639–655.
  • [45] A. Tayebi, S. Berber, and A. Swain: Performance analysis of chaotic DSSS-CDMA synchronization under jamming attack, Circuits Syst. Signal Process, 35 (2016), 4350–4371.
  • [46] X. Xu and J. Guo: Combined equalization and demodulation of chaotic direct sequence spread spectrum signals for multipath channels, Circuits Syst. Signal Process, 32 (2013), 2957–2969.
  • [47] B. Wang, H. Xu, P. Yang, L. Liu, and J. Li: Target detection and ranging through lossy media using chaotic radar, Entropy, 17 (2015), 2082–2093.
  • [48] K. W. Wong, K. P. Man, S. Li, and X. Liao: A more secure chaotic cryptographic scheme based on the dynamic look-up table, Circuits Syst. Signal Process, 24 (2005), 571–584.
  • [49] C. Li and J. C. Sprott: Amplitude control approach for chaotic signals, Nonlinear Dynamics, 73 (2013), 1335–1341.
  • [50] C. Li and J. C. Sprott: Finding coexisting attractors using amplitude control. Nonlinear Dynamics, 78 (2014), 2059–2064.
  • [51] C. Li and J. C. Sprott: Variable-boostable chaotic flows. Optik, 127 (2016), 10389–10398.
  • [52] L. Fortuna,M. Frasca, andM.G.Xibilia:Chua’sCircuit Implementation: Yesterday, Today and Tomorrow,World Scientific, Singapore, 2009.
  • [53] A. Buscarino, L. Fortuna, M. Frasca, and G. Sciuto: A Concise Guide to Chaotic Electronic Circuits, Springer, Berlin, Germany, 2014.
  • [54] S. Vaidyanathan and A. Rhif: A novel four-leaf chaotic system, its control and synchronisation via integral slidingmode control, International Journal of Modelling, Identification and Control, 28(1) (2017), 28–39.
  • [55] S. Vaidyanathan, A. T. Azar, and A. Boulkroune: A novel 4-D hyperchaotic system with two quadratic nonlinearities and its adaptive synchronisation, International Journal of Automation and Control, 12 (2018), 5–26.
  • [56] S. Boccaletti, C. Grebogi, Y. C. Lai, H. Mancini, and D. Maza: The control of chaos: theory and applications, Physics Reports, 329 (2000), 103–197.
  • [57] Z. Vukic, L. Kuljaca, D. Donlagic, and S. Tesnjak: Nonlinear Control Systems, Marcel Dekker, New York, USA, 2003.
  • [58] S. Banerjee: Chaos Syncrhonization and Cryptography for Secure Communications, IGI Global, USA, 2010.
  • [59] C. K. Volos, I. M. Kyprianidis, and I. N. Stouboulos: Image encryption process based on chaotic synchronization phenomena, Signal Processing, 93 (2013), 1328–1340.
  • [60] A. Ouannas, Z. Odibat, and T. Hayat: Fractional analysis of co-existence of some types of chaos synchronization, Chaos, Solitons & Fractals, 105 (2017), 215–223.
Uwagi
PL
Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2019).
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-898f05eb-8d56-4a72-b6db-28f92a38fc0e
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