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Synchronization and anti-synchronization of Lu and Bhalekar–Gejji chaotic systems using nonlinear active control

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  • Singh, Piyush Pratap
  • Singh, Jay Prakash
  • Roy, B.K.

Abstract

This paper aims at synchronization and anti-synchronization between Lu chaotic system, a member of unified chaotic system, and recently developed Bhalekar–Gejji chaotic system, a system which cannot be derived from the member of unified chaotic system. These synchronization and anti-synchronization have been achieved by using nonlinear active control since the parameters of both the systems are known. Lyapunov stability theory is used and required condition is derived to ensure the stability of error dynamics. Controller is designed by using the sum of relevant variables in chaotic systems. Simulation results suggest that proposed scheme is working satisfactorily.

Suggested Citation

  • Singh, Piyush Pratap & Singh, Jay Prakash & Roy, B.K., 2014. "Synchronization and anti-synchronization of Lu and Bhalekar–Gejji chaotic systems using nonlinear active control," Chaos, Solitons & Fractals, Elsevier, vol. 69(C), pages 31-39.
    • Handle: RePEc:eee:chsofr:v:69:y:2014:i:c:p:31-39
    DOI: 10.1016/j.chaos.2014.09.005
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    References listed on IDEAS

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    1. Li, Guo-Hui & Zhou, Shi-Ping, 2007. "Anti-synchronization in different chaotic systems," Chaos, Solitons & Fractals, Elsevier, vol. 32(2), pages 516-520.
    2. Ayub Khan & Ram Pravesh Prasad, 2012. "Anti-Synchronization of Pan and Lorenz-Lu-Liu-Cai Chaotic Systems by Active Nonlinear Control," International Journal of Artificial Life Research (IJALR), IGI Global, vol. 3(2), pages 15-25, April.
    3. Li, Wenlin & Chen, Xiuqin & Zhiping, Shen, 2008. "Anti-synchronization of two different chaotic systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(14), pages 3747-3750.
    4. Wang, Yan-Wu & Guan, Zhi-Hong, 2006. "Generalized synchronization of continuous chaotic system," Chaos, Solitons & Fractals, Elsevier, vol. 27(1), pages 97-101.
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    Cited by:

    1. Singh, Piyush Pratap & Roy, Binoy Krishna, 2022. "Chaos and multistability behaviors in 4D dissipative cancer growth/decay model with unstable line of equilibria," Chaos, Solitons & Fractals, Elsevier, vol. 161(C).
    2. J. Humberto Pérez-Cruz, 2018. "Stabilization and Synchronization of Uncertain Zhang System by Means of Robust Adaptive Control," Complexity, Hindawi, vol. 2018, pages 1-19, December.
    3. Rehan, Muhammad & Tufail, Muhammad & Hong, Keum-Shik, 2016. "Delay-range-dependent synchronization of drive and response systems under input delay and saturation," Chaos, Solitons & Fractals, Elsevier, vol. 87(C), pages 197-207.
    4. Singh, Jay Prakash & Roy, B.K., 2016. "The nature of Lyapunov exponents is (+, +, −, −). Is it a hyperchaotic system?," Chaos, Solitons & Fractals, Elsevier, vol. 92(C), pages 73-85.
    5. Singh, Jay Prakash & Roy, Binoy Krishna & Jafari, Sajad, 2018. "New family of 4-D hyperchaotic and chaotic systems with quadric surfaces of equilibria," Chaos, Solitons & Fractals, Elsevier, vol. 106(C), pages 243-257.
    6. Deshpande, Amey S. & Daftardar-Gejji, Varsha & Sukale, Yogita V., 2017. "On Hopf bifurcation in fractional dynamical systems," Chaos, Solitons & Fractals, Elsevier, vol. 98(C), pages 189-198.
    7. Runzi Luo & Haipeng Su & Yanhui Zeng, 2017. "Chaos Control and Synchronization via Switched Output Control Strategy," Complexity, Hindawi, vol. 2017, pages 1-11, January.
    8. J. Humberto Pérez-Cruz & Pedro A. Tamayo-Meza & Maricela Figueroa & Ramón Silva-Ortigoza & Mario Ponce-Silva & R. Rivera-Blas & Mario Aldape-Pérez, 2019. "Exponential Synchronization of Chaotic Xian System Using Linear Feedback Control," Complexity, Hindawi, vol. 2019, pages 1-10, July.
    9. Anand, Pallov & Sharma, Bharat Bhushan, 2020. "Simplified synchronizability scheme for a class of nonlinear systems connected in chain configuration using contraction," Chaos, Solitons & Fractals, Elsevier, vol. 141(C).
    10. Singh, Jay Prakash & Roy, Binoy Krishna, 2018. "Five new 4-D autonomous conservative chaotic systems with various type of non-hyperbolic and lines of equilibria," Chaos, Solitons & Fractals, Elsevier, vol. 114(C), pages 81-91.
    11. Iqbal, Muhammad & Rehan, Muhammad & Hong, Keum-Shik & Khaliq, Abdul & Saeed-ur-Rehman,, 2015. "Sector-condition-based results for adaptive control and synchronization of chaotic systems under input saturation," Chaos, Solitons & Fractals, Elsevier, vol. 77(C), pages 158-169.

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