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On chaos and projective synchronization of a fractional difference map with no equilibria using a fuzzy-based state feedback control

Author

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  • Zambrano-Serrano, Ernesto
  • Bekiros, Stelios
  • Platas-Garza, Miguel A.
  • Posadas-Castillo, Cornelio
  • Agarwal, Praveen
  • Jahanshahi, Hadi
  • Aly, Ayman A.

Abstract

In this paper, by considering the Caputo-like delta difference definition, a fractional difference order map with chaotic dynamics and with no equilibria is proposed. The complex dynamical behaviors associated with fractional difference order maps are analyzed employing the phase portraits, bifurcations diagrams, and Lyapunov exponents. The complexity of the sequence generated by the chaotic difference map is studied using the permutation entropy approach. Afterwards, projective synchronization of the systems is investigated. Fuzzy logic engines as intelligent schemes are strong tools for control of various systems. However, studies that apply fuzzy logic engines for control of fractional-order discrete-time systems are rare. Hence, in the current study, by taking advantages of fuzzy systems, a new controller is proposed for the fractional-order discrete-time map. The fuzzy logic engine is implemented in order to enhance the performance and agility of the proposed control technique. The stability of the closed-loop systems and asymptotic convergence of the projective synchronization error based on the proposed control scheme are proven. Finally, numerical simulations which clearly confirm that the offered control technique is able to push the states of the fractional-order discrete-time system to the desired value in a short period of time are presented.

Suggested Citation

  • Zambrano-Serrano, Ernesto & Bekiros, Stelios & Platas-Garza, Miguel A. & Posadas-Castillo, Cornelio & Agarwal, Praveen & Jahanshahi, Hadi & Aly, Ayman A., 2021. "On chaos and projective synchronization of a fractional difference map with no equilibria using a fuzzy-based state feedback control," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 578(C).
    • Handle: RePEc:eee:phsmap:v:578:y:2021:i:c:s0378437121003733
    DOI: 10.1016/j.physa.2021.126100
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    1. Chu, Yu-Ming & Bekiros, Stelios & Zambrano-Serrano, Ernesto & Orozco-López, Onofre & Lahmiri, Salim & Jahanshahi, Hadi & Aly, Ayman A., 2021. "Artificial macro-economics: A chaotic discrete-time fractional-order laboratory model," Chaos, Solitons & Fractals, Elsevier, vol. 145(C).
    2. Zhou, Shuang-Shuang & Jahanshahi, Hadi & Din, Qamar & Bekiros, Stelios & Alcaraz, Raúl & Alassafi, Madini O. & Alsaadi, Fawaz E. & Chu, Yu-Ming, 2021. "Discrete-time macroeconomic system: Bifurcation analysis and synchronization using fuzzy-based activation feedback control," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).
    3. Lu, Jun Guo & Chen, Guanrong, 2006. "A note on the fractional-order Chen system," Chaos, Solitons & Fractals, Elsevier, vol. 27(3), pages 685-688.
    4. Li, Jun-Feng & Jahanshahi, Hadi & Kacar, Sezgin & Chu, Yu-Ming & Gómez-Aguilar, J.F. & Alotaibi, Naif D. & Alharbi, Khalid H., 2021. "On the variable-order fractional memristor oscillator: Data security applications and synchronization using a type-2 fuzzy disturbance observer-based robust control," Chaos, Solitons & Fractals, Elsevier, vol. 145(C).
    5. Ge, Zheng-Ming & Ou, Chan-Yi, 2007. "Chaos in a fractional order modified Duffing system," Chaos, Solitons & Fractals, Elsevier, vol. 34(2), pages 262-291.
    6. Jahanshahi, Hadi & Munoz-Pacheco, Jesus M. & Bekiros, Stelios & Alotaibi, Naif D., 2021. "A fractional-order SIRD model with time-dependent memory indexes for encompassing the multi-fractional characteristics of the COVID-19," Chaos, Solitons & Fractals, Elsevier, vol. 143(C).
    7. He, Shaobo & Sun, Kehui & Wang, Huihai, 2016. "Multivariate permutation entropy and its application for complexity analysis of chaotic systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 461(C), pages 812-823.
    8. Li, Chunguang & Chen, Guanrong, 2004. "Chaos and hyperchaos in the fractional-order Rössler equations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 341(C), pages 55-61.
    9. Jahanshahi, Hadi & Sajjadi, Samaneh Sadat & Bekiros, Stelios & Aly, Ayman A., 2021. "On the development of variable-order fractional hyperchaotic economic system with a nonlinear model predictive controller," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).
    10. Chen, Shu-Bo & Jahanshahi, Hadi & Alhadji Abba, Oumate & Solís-Pérez, J.E. & Bekiros, Stelios & Gómez-Aguilar, J.F. & Yousefpour, Amin & Chu, Yu-Ming, 2020. "The effect of market confidence on a financial system from the perspective of fractional calculus: Numerical investigation and circuit realization," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    11. Sun, Bo & Cao, Yuting & Guo, Zhenyuan & Yan, Zheng & Wen, Shiping, 2020. "Synchronization of discrete-time recurrent neural networks with time-varying delays via quantized sliding mode control," Applied Mathematics and Computation, Elsevier, vol. 375(C).
    12. Jahanshahi, Hadi & Yousefpour, Amin & Munoz-Pacheco, Jesus M. & Kacar, Sezgin & Pham, Viet-Thanh & Alsaadi, Fawaz E., 2020. "A new fractional-order hyperchaotic memristor oscillator: Dynamic analysis, robust adaptive synchronization, and its application to voice encryption," Applied Mathematics and Computation, Elsevier, vol. 383(C).
    13. Jahanshahi, Hadi & Orozco-López, Onofre & Munoz-Pacheco, Jesus M. & Alotaibi, Naif D. & Volos, Christos & Wang, Zhen & Sevilla-Escoboza, R. & Chu, Yu-Ming, 2021. "Simulation and experimental validation of a non-equilibrium chaotic system," Chaos, Solitons & Fractals, Elsevier, vol. 143(C).
    14. Gafiychuk, V. & Datsko, B. & Meleshko, V., 2008. "Analysis of fractional order Bonhoeffer–van der Pol oscillator," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(2), pages 418-424.
    15. Soradi-Zeid, Samaneh & Jahanshahi, Hadi & Yousefpour, Amin & Bekiros, Stelios, 2020. "King algorithm: A novel optimization approach based on variable-order fractional calculus with application in chaotic financial systems," Chaos, Solitons & Fractals, Elsevier, vol. 132(C).
    16. Wang, Lingyu & Sun, Kehui & Peng, Yuexi & He, Shaobo, 2020. "Chaos and complexity in a fractional-order higher-dimensional multicavity chaotic map," Chaos, Solitons & Fractals, Elsevier, vol. 131(C).
    17. Yousefpour, Amin & Jahanshahi, Hadi & Munoz-Pacheco, Jesus M. & Bekiros, Stelios & Wei, Zhouchao, 2020. "A fractional-order hyper-chaotic economic system with transient chaos," Chaos, Solitons & Fractals, Elsevier, vol. 130(C).
    18. Wang, Shaojie & Bekiros, Stelios & Yousefpour, Amin & He, Shaobo & Castillo, Oscar & Jahanshahi, Hadi, 2020. "Synchronization of fractional time-delayed financial system using a novel type-2 fuzzy active control method," Chaos, Solitons & Fractals, Elsevier, vol. 136(C).
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    2. Surendar, R. & Muthtamilselvan, M. & Ahn, Kyubok, 2024. "Stochastic disturbance with finite-time chaos stabilization and synchronization for a fractional-order nonautonomous hybrid nonlinear complex system via a sliding mode control," Chaos, Solitons & Fractals, Elsevier, vol. 181(C).
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