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A new multi-stable chaotic hyperjerk system, its special features, circuit realization, control and synchronization

Treść / Zawartość
Identyfikatory
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
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.
Rocznik
Strony
23--45
Opis fizyczny
Bibliogr. 42 poz., rys., wykr., wzory
Twórcy
  • Nonlinear Systems and Applications, Faculty of Electrical and Electronics Engineering, Ton Duc Thang University, Ho Chi Minh City, Vietnam
  • Division of Dynamics, Lodz University of Technology, Stefanowskiego 1/15, 90-924 Lodz, Poland
  • School of Electrical and Communication Engineering, Vel Tech University, 400 Feet Outer Ring Road, Vel Nagar, Chennai, India
  • Physics Department, Aristotle University of Thessaloniki, Thessaloniki, Greece
autor
  • Biomedical Engineering Department, Amirkabir University of Technology, Tehran 15875-4413, Iran
  • Division of Dynamics, Lodz University of Technology, Stefanowskiego 1/15, 90-924 Lodz, Poland
Bibliografia
  • [1] S. Behnia, J. Ziaei, and M. Khodavirdizadeh: Detecting a pronounced delocalized state in third-harmonic generation phenomenon; a quantum chaos approach. Optics Communications, 416 (2018), 19–24.
  • [2] V.-T. Pham, C. Volos, S. Jafari, X. Wang, and S. Vaidyanathan: Hidden hyperchaotic attractor in a novel simple memristive neural network, Optoelectronics and Advanced Materials – Rapid Communications, 8 (2014), 1157–1163.
  • [3] 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.
  • [4] 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.
  • [5] S. Vaidyanathan and S. Rasappan: Hybrid synchronization of hyper-chaotic Qi and Lu systems by nonlinear control, Communications in Computer and Information Science, 131 (2011), 585–593.
  • [6] V.-T. Pham, S. Jafari, C. Volos, and L. Fortuna: Simulation and experimental implementation of a line-equilibrium system without linear term, Chaos, Solitons and Fractals, 120 (2019), 213–221.
  • [7] 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.
  • [8] G. A. Al-Suhail, F. R. Tahir, M. H. Abd, V.-T. Pham, and L. Fortuna: Modelling of long-wave chaotic radar system for anti-stealth applications, Communications in Nonlinear Science and Numerical Simulation, 57 (2018), 80–96.
  • [9] 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.
  • [10] S. Vaidyanathan: Adaptive control and synchronization design for the Lu-Xiao chaotic system, Lecture Notes in Electrical Engineering, 131 (2013), 319–327.
  • [11] S. Vaidyanathan: Output regulation of the forced Van der Pol chaotic oscillator via adaptive control method, International Journal of PharmTech Research, 8(6) (2015), 106–116.
  • [12] 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.
  • [13] V. T. Pham, S. Vaidyanathan, C. K. Volos, S. Jafari, N. V. Kuznetsov, and T. M. Hoang: A novel memristive time-delay chaotic system without equilibrium points, European Physical Journal: Special Topics, 225(1) (2016), 127–136.
  • [14] V. T. Pham, S. Jafari, S. Vaidyanathan, C. Volos, and X. Wang: A novel memristive neural network with hidden attractors and its circuitry implementation, Science China Technological Sciences, 59(3) (2016), 358–363.
  • [15] S. Vaidyanathan: Adaptive control of the FitzHugh-Nagumo chaotic neuron model, International Journal of PharmTech Research, 8(6) (2015), 117–127.
  • [16] S. Vaidyanathan: Chaos in neurons and adaptive control of Birkhoff-Shaw strange chaotic attractor, International Journal of PharmTech Research, 8(5) (2015), 956–963.
  • [17] S. Vaidyanathan: Global chaos synchronization of chemical chaotic reactors via novel sliding mode control method, International Journal of ChemTech Research, 8(7) (2015), 209–221.
  • [18] 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, Applied Mathematics and Computation, 276 (2016), 200–217.
  • [19] V. T. Pham, S. Vaidyanathan, C. Volos, S. Jafari, and S. T. Kingni: A noequilibrium hyperchaotic system with a cubic nonlinear term, Optik, 127 (2016), 3259–3265.
  • [20] S. Vaidyanathan, C. Volos, V.-T. Pham, K. Madhavan, and B. A. Idowu: Adaptive backstepping control, synchronization and circuit simulation of a 3-D novel jerk chaotic system with two hyperbolic sinusoidal nonlinearities, Archives of Control Sciences, 24 (2014), 257–285.
  • [21] S. Vaidyanathan, A. Sambas, M. Mamat and M. Sanjaya W. S.: 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.
  • [22] S. Schot: Jerk: the time rate of change of acceleration, American Journal of Physics, 46 (1978), 1090–1094.
  • [23] B. Munmuangsaen, B. Srisuchinwong, and J. C. Sprott: Generalization of the simplest autonomous chaotic system, Physics Letters A, 375 (2011), 1445–1450.
  • [24] J. C. Sprott: A new chaotic jerk circuit, IEEE Transactions on Circuits and Systems-II: Express Briefs, 58 (2011), 240–243.
  • [25] K. H. Sun and J. C. Sprott: A simple jerk system with piecewise exponential nonlinearity, International Journal of Nonlinear Science and Numerical Simulation, 10 (2009), 1443–1450.
  • [26] 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.
  • [27] V.-T. Pham , S. Jafari, C. Volos, and T. Kapitaniak: Coexistence of hidden chaotic attractors in a novel no-equilibrium system, Nonlinear Dynamics, 87 (2017), 2001–2010.
  • [28] V.-T. Pham, C. Volos, S. T. Kingni, T. Kapitaniak, and S. Jafari: Bistable hidden attractors in a novel chaotic system with hyperbolic sine equilibrium, Circuit, Systems, and Signal Processing, 37 (2018), 1028–1043.
  • [29] V.-T. Pham, C. Volos, S. Jafari, and T. Kapitaniak: A novel cubic-equilibrium chaotic system with coexisting hidden attractors: Analysis and circuit implementation, Journal of Circuits, Systems, and Computers, 27 (2018), 1850066.
  • [30] P. Loudopop, M. Kountchou, H. Fotsin and S. Bowong: Practical finite-time synchronization of jerk systems: theory and experiment, Nonlinear Dynamics, 78 (2014), 597–607.
  • [31] K. E. Chlouverakis and J. C. Sprott: Chaotic hyperjerk systems, Chaos, Solitons & Fractals, 28 (2006), 739–746.
  • [32] B. Munmuangsaen and B. Srisuchinwong: Elementary chaotic snap flows, Chaos, Solitons & Fractals, 44 (2011), 995–1003.
  • [33] B. Bao, X. Zou, Z. Liu, and F. Hu: Generalized memory element and chaotic memory system, International Journal of Bifurcation and Chaos, 23(8) (2013), 1350135.
  • [34] S. Vaidyanathan: Analysis, adaptive control and synchronization of a novel 4-D hyperchaotic hyperjerk system via backstepping control method, Archives of Control Sciences, 26(3), (2016), 311–338.
  • [35] F. Y. Dalkiran and J. C. Sprott: Simple chaotic hyperjerk system, International Journal of Bifurcation and Chaos, 26(11) (2016), 1650189.
  • [36] V.-T. Pham, S. Vaidyanathan, C. Volos, S. Jafari, F. E. Alsaadi, and F. E. Alsaadis: Chaos in a simple snap system with only one nonlinearity, its adaptive control and real circuit design, Archives of Control Sciences, 29(1) (2019), 73–96.
  • [37] C. Li and J. C. Sprott: Amplitude control approach for chaotic signals, Nonlinear Dynamics, 73 (2013), 1335–1341.
  • [38] C. Li and J. C. Sprott: Finding coexisting attractors using amplitude control. Nonlinear Dynamics, 78 (2014), 2059–2064.
  • [39] C. Li and J. C. Sprott: Variable-boostable chaotic flows. Optik, 127 (2016), 10389–10398.
  • [40] V.-T. Pham, A. Akgul, C. Volos, S. Jafari, and T. Kapitaniak: Dynamics and circuit realization of a no-equilibrium chaotic system with a boostable variable, International Journal of Electronics and Communications, 78 (2017), 134–140.
  • [41] L. Fortuna, M. Frasca, and M. G. Xibilia: Chua’s Circuit Implementation: Yesterday, Today and Tomorrow, World Scientific, Singapore, 2009.
  • [42] A. Buscarino, L. Fortuna, M. Frasca, and G. Sciuto: A Concise Guide to Chaotic Electronic Circuits, Springer, Berlin, Germany, 2014.
Uwagi
EN
1. This work has been supported by the Polish National Science Centre, MAESTRO Programme-Project No 2013/08/A/ST8/00/780.
PL
2. Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2020).
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-e6ae0498-1c5b-4c4c-937f-ed2809b5408c
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