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Chaos in the delay logistic equation with discontinuous delays

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  • Sen, Ayan
  • Mukherjee, Debasis

Abstract

This paper analyzes a delay logistic equation which models a feedback control problem. Interval map associated to the system is derived. By calculating Lyapunov exponent, we indicate stable orbit and chaotic phenomenon respectively. The results are verified through computer simulation. We identify the parameter which controls the dynamics.

Suggested Citation

  • Sen, Ayan & Mukherjee, Debasis, 2009. "Chaos in the delay logistic equation with discontinuous delays," Chaos, Solitons & Fractals, Elsevier, vol. 40(5), pages 2126-2132.
    • Handle: RePEc:eee:chsofr:v:40:y:2009:i:5:p:2126-2132
    DOI: 10.1016/j.chaos.2007.10.019
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    References listed on IDEAS

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    1. Peng, Mingshu, 2005. "Multiple bifurcations and periodic “bubbling” in a delay population model," Chaos, Solitons & Fractals, Elsevier, vol. 25(5), pages 1123-1130.
    2. Sun, Chengjun & Cao, Zhijie & Lin, Yiping, 2007. "Analysis of stability and Hopf bifurcation for a viral infectious model with delay," Chaos, Solitons & Fractals, Elsevier, vol. 33(1), pages 234-245.
    3. Berezowski, M. & Fudała, E., 2006. "Bifurcation analysis of the statics and dynamics of a logistic model with two delays," Chaos, Solitons & Fractals, Elsevier, vol. 28(2), pages 543-554.
    4. Sun, Chengjun & Han, Maoan & Lin, Yiping, 2007. "Analysis of stability and Hopf bifurcation for a delayed logistic equation," Chaos, Solitons & Fractals, Elsevier, vol. 31(3), pages 672-682.
    5. Chen, Yuanyuan & Yu, Jiang & Sun, Chengjun, 2007. "Stability and Hopf bifurcation analysis in a three-level food chain system with delay," Chaos, Solitons & Fractals, Elsevier, vol. 31(3), pages 683-694.
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