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Analysis and Application Using Quad Compound Combination Anti-synchronization on Novel Fractional-Order Chaotic System

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Abstract

In this manuscript, a novel fractional-order chaotic model has been investigated. The characteristic dynamics of the model have been investigated using various tools such as Lyapunov dynamics, bifurcation diagrams, equilibrium point analysis, Kaplan York dimension, existence and uniqueness of solution. The Lyapunov spectrum, bifurcation diagrams and attractors are discussed over a range of fractional order of 0.8 to 1. The considered system is synchronized by using a novel technique quad compound combination anti-synchronization using two control methods, viz. nonlinear and adaptive sliding mode technique. The obtained results of synchronization are compared with some existing literature and also illustrated its application in secure communication.

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References

  1. Wu, Y.; Noonan, J.P.; Yang, G.; Jin, H.: Image encryption using the two-dimensional logistic chaotic map. J. Electron. Imaging 21(1), 013–014 (2012)

    Article  Google Scholar 

  2. Khan, A.; Lone S.J.; Trikha P.: Analysis of a novel 3-D fractional order chaotic system. ICPECA, pp. 1-6, IEEE (2019)

  3. Wong, K.; Man, K.P.; Li, S.; Liao, X.: A more secure chaotic cryptographic scheme based on the dynamic look-up table. Circuits, Syst. Signal Process. 24(5), 571–584 (2005)

    Article  MathSciNet  Google Scholar 

  4. Khan, A.; Trikha, P.: Study of earth’s changing polarity using compound difference synchronization. GEM-Int. J. Geomath. 11(1), 7 (2020)

    Article  MathSciNet  Google Scholar 

  5. Baleanu, D.; Jajarmi, A.; Mohammadi, H.; Rezapour, S.: A new study on the mathematical modelling of human liver with Caputo–Fabrizio fractional derivative. Chaos, Solitons and Fractals 134, 109705 (2020)

    Article  MathSciNet  Google Scholar 

  6. Inan, B..; Osman, M.S.; Turgut, A.k.; Baleanu, D.: Analytical and numerical solutions of mathematical biology models: The Newell–Whitehead–Segel and Allen–Cahn equations, Mathematical Methods in the Applied Sciences, Wiley Online Library (2019)

  7. Baleanu, D.; Jajarmi, A.; Sajjadi, S.S.; Asad, J.H.: The fractional features of a harmonic oscillator with position-dependent mass. Commun. Theor. Phys. 72(5), 055002 (2020)

    Article  MathSciNet  Google Scholar 

  8. Baleanu, D.; Etemad, S.; Rezapour, S.: A hybrid Caputo fractional modeling for thermostat with hybrid boundary value conditions. Bound. Value Prob. 2020(1), 1–16 (2020)

    Article  MathSciNet  Google Scholar 

  9. Sun, J.; Li, N.; Wang, Y.; Wang, W.: A novel chaotic system and its modified compound synchronization. Fundam. Inform. 164(2–3), 259–275 (2019)

    Article  MathSciNet  Google Scholar 

  10. Vaidyanathan, S.: Analysis, control and synchronisation of a six-term novel chaotic system with three quadratic nonlinearities. Int. J. Modell. Identif. Control 22(1), 41–53 (2014)

    Article  Google Scholar 

  11. Vaidyanathan, S.; Rajagopal, K.; Volos, C.K.; Kyprianidis, I.M.; Stouboulos, I.N.: Analysis, adaptive control and synchronization of a seven-term novel 3-D chaotic system with three quadratic nonlinearities and its digital implementation in LabVIEW. J. Eng. Sci. Technol. Rev. 8(2), 130–141 (2015)

    Article  Google Scholar 

  12. Vaidyanathan, S.; Volos, C.K.; Pham, V.T.: Analysis, adaptive control and adaptive synchronization of a nine-term novel 3-D chaotic system with four quadratic nonlinearities and its circuit simulation. J. Eng. Sci. Technol. Rev. 8(2), 181–191 (2015)

    Google Scholar 

  13. Zhang, S.; Zeng, Y.: A simple Jerk-like system without equilibrium: Asymmetric coexisting hidden attractors, bursting oscillation and double full Feigenbaum remerging trees. Chaos, Solitons and Fractals 120, 25–40 (2019)

    Article  MathSciNet  Google Scholar 

  14. Pecora, L.M.; Carroll, T.L.: Synchronization in chaotic systems. Phys. Rev. Lett. 64(8), 821 (1990)

    Article  MathSciNet  Google Scholar 

  15. Sun, J.; Shen, Y.; Yin, Q.; Yu, C.: Compound synchronization of four memristor chaotic oscillator systems and secure communication. Chaos: An Interdiscip. J. Nonlinear Sci. 23(1), 013140 (2013)

    Article  MathSciNet  Google Scholar 

  16. Sun, J.; Yin, Q.; Shen, Y.: Compound synchronization for four chaotic systems of integer order and fractional order. EPL (Europhys. Lett.) 106(4), 40005 (2014)

    Article  Google Scholar 

  17. Dongmo, E.D.; Ojo, K.S.; Woafo, P.; Njah, A.N.: Difference Synchronization of identical & Non-identical chaotic & hyper chaotic systems of different orders using active backstepping design. J. Comput. Nonlinear Dyn. (2018). https://doi.org/10.1115/1.4039626

  18. Runzi, L.; Yinglan, W.; Shucheng, D.: Combination synchronization of three classic chaotic systems using active backstepping design. Chaos: An Interdiscip. J. Nonlinear Sci. 21(4), 043114 (2011)

    Article  Google Scholar 

  19. Li, B.; Zhou, X.; Wang, Y.: Combination synchronization of three different fractional-order delayed chaotic systems. Complexity 2019, 5184032 (2019). https://doi.org/10.1155/2019/5184032

  20. Rosenblum, M.G.; Pikovsky, A.S.; Kurths, J.: Phase synchronization of chaotic oscillators. Phys. Rev. Lett. 76(11), 1804 (1996)

    Article  Google Scholar 

  21. Rosenblum, M.G.; Pikovsky, A.S.; Kurths, J.: From phase to lag synchronization in coupled chaotic oscillators. Phys. Rev. E. 78(22), 4193 (1997)

    MATH  Google Scholar 

  22. Zhang, B.; Deng, F.: Double-compound synchronization of six memristor-based Lorenz systems. Nonlinear Dyn. 77(4), 1519–1530 (2014)

    Article  Google Scholar 

  23. Yadav, V.K.; Prasad, G.; Srivastava, M.; Das, S.: Triple compound synchronization among eight chaotic systems with external disturbances via nonlinear approach. Differ. Equ. Dyn. Syst. pp. 1–24 (2019)

  24. Karimi, S.; Effati, S.; Ghane, F.H.: The synchronization of chaotic systems applying the parallel synchronization method. Phys. Scripta 94(10), 105215 (2019)

    Article  Google Scholar 

  25. Khan, A.; Trikha, P.; Jahanzaib, L.S.: Dislocated hybrid synchronization via. tracking control & parameter estimation methods with application, Int. J. Model. Simul. pp. 1-11, Taylor and Francis (2020)

  26. Trikha, P.; Jahanzaib, L.S.: Secure communication: using double compound-combination hybrid synchronization, In: Proceedings of International Conference on Artificial Intelligence and Applications. pp. 81–91, Springer (2020)

  27. Khan, A.; Jahanzaib, L.S.; Trikha, P.: Fractional inverse matrix projective combination synchronization with application in secure communication, In: Proceedings of International Conference on Artificial Intelligence and Applications. pp. 93–101, Springer (2020)

  28. Wolf, A.; Swift, J.B.; Swinney, H.L.; Vastano, J.A.: Determining lyapunov exponents from a time series. Phys. D: Nonlinear Phenom. 16(3), 285–317 (1985)

    Article  MathSciNet  Google Scholar 

  29. Geist, K.; Parlitz, U.; Lauterborn, W.: Comparison of different methods for computing lyapunov exponents. Progress Theor. Phys. 83(5), 875–893 (1990)

    Article  MathSciNet  Google Scholar 

  30. Broucke, M.: One parameter bifurcation diagram for chua’s circuit. IEEE Trans. Circuits Syst. 34(2), 208–209 (1987)

    Article  MathSciNet  Google Scholar 

  31. Pham, V.-T.; Vaidyanathan, S.; Volos, C.; Jafari, S.; Alsaadi, F.E.; Alsaadi, F.E.: Chaos in a simple snap system with only one nonlinearity, its adaptive control and real circuit design. Arch. Control Sci. 29(1), 73–96 (2019). https://doi.org/10.24425/acs.2019.127524

  32. Diethelm, K.; Ford, N.J.: J. Math. Anal. Appl., vol. 265, pp. 229–248. Elsevier (2002)

  33. Matignon, D.: Stability results for fractional differential equations with applications to control processing, In: Computational Engineering in Systems Applications, vol. 2, pp. 963-968. IMACS, IEEE-SMC Lille, France (1996)

  34. Vidyasagar, M.: Nonlinear Systems Analysis, vol. 42. Siam, Philadelphia (2002)

    Book  Google Scholar 

  35. Mahmoud, G.M.; Abed-Elhameed, T.M.; Farghaly, A.: ADouble compound combination synchronization among eight n-dimensional chaotic systems. Chinese Phys. B 27(8), 080502 (2018)

    Article  Google Scholar 

  36. Khan, A.; Trikha, P.; Lone, S.J.: Secure Communication: Using synchronization on a novel fractional order chaotic system. ICPECA, pp. 1–5, IEEE (2019)

  37. Vaidyanathan, S.; Rajagopal, K.; Volos, C.K.; Kyprianidis, I.M.: Stouboulos, Analysis, adaptive control and synchronization of a seven-term novel 3-D chaotic system with three quadratic nonlinearities and its digital implementation in LabVIEW. J. Eng. Sci. Technol. Rev. 8(2), 130–141 (2015)

    Article  Google Scholar 

  38. Khan, A.; Jahanzaib, L.S.; Trikha, P.: Secure communication: using parallel synchronization technique on novel frcational order chaotic system. IFAC Papers Online 53(1), 307–312 (2020)

    Article  Google Scholar 

  39. Khan, A.; Trikha, P.: Compound difference anti-synchronization between chaotic systems of integer and fractional order. SN Appl. Sci. 1, 757 (2019). https://doi.org/10.1007/s42452-019-0776-x

    Article  Google Scholar 

  40. Sundarapandian, V.; Pehlivan, I.: Analysis, control, synchronization, and circuit design of a novel chaotic system. Math. Comput. Modell. 55(7–8), 1904–1915 (2012)

    Article  MathSciNet  Google Scholar 

  41. Sun, K.; Liu, L.; Qiu, J.; Feng, G.: Fuzzy adaptive finite-time fault-tolerant control for strict-feedback nonlinear systems. In: IEEE Transactions on Fuzzy Systems. (2020). https://doi.org/10.1109/TFUZZ.2020.296589

  42. Qiu, J.; Sun, K.; Wang, T.; Gao, H.: Observer-based fuzzy adaptive event-triggered control for pure-feedback nonlinear systems with prescribed performance. IEEE Trans. Fuzzy Syst. 27(11), 2152–2162 (2019)

    Article  Google Scholar 

  43. Qiu, J.; Sun, K.; Rudas, I.J.; Gao, H.: Command filter-based adaptive NN control for MIMO nonlinear systems with full-state constraints and actuator hysteresis, In: IEEE Transactions on Cybernetics, vol. 50, no. 7, pp. 2905–2915 (2020). https://doi.org/10.1109/TCYB.2019.2944761

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Acknowledgements

L.S.Jahanzaib (MANF-2018-19-JAM-98362,U.G.C., India) and P. Trikha (09/466(0189)/2017-EMR-I,CSIR, India) thank the agencies for providing financial support as J. R. F. and S. R. F. respectively.

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Authors and Affiliations

  1. Department of Mathematics, Jamia Millia Islamia, New Delhi, 110025, India

    Lone Seth Jahanzaib & Pushali Trikha

  2. Department of Mathematics, Cankaya University, Ögretmenler Cad, 1406530, Ankara, Turkey

    Dumitru Baleanu

  3. Institute of Space Sciences, Magurele, Bucharest, Romania

    Dumitru Baleanu

  4. Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, Taiwan

    Dumitru Baleanu

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  1. Lone Seth Jahanzaib
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  2. Pushali Trikha
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  3. Dumitru Baleanu
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Correspondence to Dumitru Baleanu.

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Jahanzaib, L.S., Trikha, P. & Baleanu, D. Analysis and Application Using Quad Compound Combination Anti-synchronization on Novel Fractional-Order Chaotic System. Arab J Sci Eng 46, 1729–1742 (2021). https://doi.org/10.1007/s13369-020-04939-z

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  • DOI: https://doi.org/10.1007/s13369-020-04939-z

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