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Fractional Order Memristor No Equilibrium Chaotic System with Its Adaptive Sliding Mode Synchronization and Genetically Optimized Fractional Order PID Synchronization

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  • Karthikeyan Rajagopal
  • Laarem Guessas
  • Anitha Karthikeyan
  • Ashokkumar Srinivasan
  • Girma Adam

Abstract

This paper introduces a fractional order memristor no equilibrium (FOMNE) chaotic system and investigates its adaptive sliding mode synchronization. Firstly the dynamic properties of the integer order memristor no equilibrium system are analyzed. The fractional order memristor no equilibrium system is then derived from the integer order model. Lyapunov exponents and bifurcation with fractional order are investigated. An adaptive sliding mode control algorithm is derived to globally synchronize the identical fractional order memristor systems and genetically optimized fractional order PID controllers are designed and used to synchronize the FOMNE systems. Finally the fractional order memristor no equilibrium system is realized using FPGA.

Suggested Citation

  • Karthikeyan Rajagopal & Laarem Guessas & Anitha Karthikeyan & Ashokkumar Srinivasan & Girma Adam, 2017. "Fractional Order Memristor No Equilibrium Chaotic System with Its Adaptive Sliding Mode Synchronization and Genetically Optimized Fractional Order PID Synchronization," Complexity, Hindawi, vol. 2017, pages 1-19, March.
    • Handle: RePEc:hin:complx:1892618
    DOI: 10.1155/2017/1892618
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    References listed on IDEAS

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    1. Idowu, B.A. & Vincent, U.E. & Njah, A.N., 2009. "Synchronization of chaos in non-identical parametrically excited systems," Chaos, Solitons & Fractals, Elsevier, vol. 39(5), pages 2322-2331.
    2. Wang, Sha & Yu, Yongguang & Diao, Miao, 2010. "Hybrid projective synchronization of chaotic fractional order systems with different dimensions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(21), pages 4981-4988.
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    Cited by:

    1. Karthikeyan Rajagopal & Yesgat Admassu & Riessom Weldegiorgis & Prakash Duraisamy & Anitha Karthikeyan, 2019. "Chaotic Dynamics of an Airfoil with Higher-Order Plunge and Pitch Stiffnesses in Incompressible Flow," Complexity, Hindawi, vol. 2019, pages 1-10, October.
    2. Kuate, Paul Didier Kamdem & Tchendjeu, Achille Ecladore Tchahou & Fotsin, Hilaire, 2020. "A modified Rössler prototype-4 system based on Chua’s diode nonlinearity : Dynamics, multistability, multiscroll generation and FPGA implementation," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    3. Adel Ouannas & Xiong Wang & Viet-Thanh Pham & Toufik Ziar, 2017. "Dynamic Analysis of Complex Synchronization Schemes between Integer Order and Fractional Order Chaotic Systems with Different Dimensions," Complexity, Hindawi, vol. 2017, pages 1-12, June.
    4. Laarem, Guessas, 2021. "A new 4-D hyper chaotic system generated from the 3-D Rösslor chaotic system, dynamical analysis, chaos stabilization via an optimized linear feedback control, it’s fractional order model and chaos sy," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    5. Qifeng Fu & Xuemei Xu & Chuwen Xiao, 2022. "LQR Chaos Synchronization for a Novel Memristor-Based Hyperchaotic Oscillator," Mathematics, MDPI, vol. 11(1), pages 1-16, December.
    6. Nazarimehr, Fahimeh & Rajagopal, Karthikeyan & Khalaf, Abdul Jalil M. & Alsaedi, Ahmed & Pham, Viet-Thanh & Hayat, Tasawar, 2018. "Investigation of dynamical properties in a chaotic flow with one unstable equilibrium: Circuit design and entropy analysis," Chaos, Solitons & Fractals, Elsevier, vol. 115(C), pages 7-13.
    7. Wei, Zhouchao & Akgul, Akif & Kocamaz, Uğur Erkin & Moroz, Irene & Zhang, Wei, 2018. "Control, electronic circuit application and fractional-order analysis of hidden chaotic attractors in the self-exciting homopolar disc dynamo," Chaos, Solitons & Fractals, Elsevier, vol. 111(C), pages 157-168.
    8. Balamurali Ramakrishnan & Victor Kamdoum Tamba & Hayder Natiq & Alex Stephane Kemnang Tsafack & Anitha Karthikeyan, 2022. "Dynamical analysis of autonomous Josephson junction jerk oscillator with cosine interference term embedded in FPGA and investigation of its collective behavior in a network," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 95(9), pages 1-12, September.
    9. 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).
    10. Bocheng Bao & Aihuang Hu & Han Bao & Quan Xu & Mo Chen & Huagan Wu, 2018. "Three-Dimensional Memristive Hindmarsh–Rose Neuron Model with Hidden Coexisting Asymmetric Behaviors," Complexity, Hindawi, vol. 2018, pages 1-11, February.

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