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Multiple delay Rössler system—Bifurcation and chaos control

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  • Ghosh, Dibakar
  • Chowdhury, A. Roy
  • Saha, Papri

Abstract

Multiple delayed Rössler system is analyzed from the view point of stability and chaos control. Usually these systems occur in active sensing problems where a signal is transmitted and received at a later time. Analytical and numerical results are obtained from the basic characteristic equation, using the Routh–Hurwitz criterion and Sturm sequences. The bifurcation pattern as the delay increases is displayed in detail, finally leading to chaos. In the second half we analyze the structure of the unstable periodic orbits and construct the controller which gets back the system to periodic state. Quantitative measure of the accuracy of the computation is obtained through the use of conditional Lyapunov exponent. At this point a Galerkin projection technique is used, which sets up a system of ODE in place of the delayed system, and makes the computation much simpler. Importance of this analysis is due to the role of the delay terms in the generation of the attractor, various bifurcation scenario, along with their control.

Suggested Citation

  • Ghosh, Dibakar & Chowdhury, A. Roy & Saha, Papri, 2008. "Multiple delay Rössler system—Bifurcation and chaos control," Chaos, Solitons & Fractals, Elsevier, vol. 35(3), pages 472-485.
    • Handle: RePEc:eee:chsofr:v:35:y:2008:i:3:p:472-485
    DOI: 10.1016/j.chaos.2006.05.058
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    Cited by:

    1. Yang, Jihua & Zhao, Liqin, 2015. "Bifurcation analysis and chaos control of the modified Chua’s circuit system," Chaos, Solitons & Fractals, Elsevier, vol. 77(C), pages 332-339.
    2. Ahmed A. Abd El-Latif & Janarthanan Ramadoss & Bassem Abd-El-Atty & Hany S. Khalifa & Fahimeh Nazarimehr, 2022. "A Novel Chaos-Based Cryptography Algorithm and Its Performance Analysis," Mathematics, MDPI, vol. 10(14), pages 1-22, July.
    3. Zandi-Mehran, Nazanin & Jafari, Sajad & Golpayegani, Seyed Mohammad Reza Hashemi, 2020. "Signal separation in an aggregation of chaotic signals," Chaos, Solitons & Fractals, Elsevier, vol. 138(C).
    4. Serrano, Fernando E. & Ghosh, Dibakar, 2022. "Robust stabilization and synchronization in a network of chaotic systems with time-varying delays," Chaos, Solitons & Fractals, Elsevier, vol. 159(C).
    5. Poria, Swarup & Poria, Anindita Tarai & Chatterjee, Prasanta, 2009. "Synchronization threshold of a coupled n-dimensional time-delay system," Chaos, Solitons & Fractals, Elsevier, vol. 41(3), pages 1123-1124.

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