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Chaos in temporarily destabilized regular systems with the slow passage effect

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  • Perc, Matjaž
  • Marhl, Marko

Abstract

We provide evidences for chaotic behaviour in temporarily destabilized regular systems. In particular, we focus on time-continuous systems with the slow passage effect. The extreme sensitivity of the slow passage phase enables the existence of long chaotic transients induced by random pulsatile perturbations, thereby evoking chaotic behaviour in an initially regular system. We confirm the chaotic behaviour of the temporarily destabilized system by calculating the largest Lyapunov exponent. Moreover, we show that the newly obtained unstable periodic orbits can be easily controlled with conventional chaos control techniques, thereby guaranteeing a rich diversity of accessible dynamical states that is usually expected only in intrinsically chaotic systems. Additionally, we discuss the biological importance of presented results.

Suggested Citation

  • Perc, Matjaž & Marhl, Marko, 2006. "Chaos in temporarily destabilized regular systems with the slow passage effect," Chaos, Solitons & Fractals, Elsevier, vol. 27(2), pages 395-403.
    • Handle: RePEc:eee:chsofr:v:27:y:2006:i:2:p:395-403
    DOI: 10.1016/j.chaos.2005.03.045
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    Cited by:

    1. Tam, Lap Mou & Si Tou, Wai Meng, 2008. "Parametric study of the fractional-order Chen–Lee system," Chaos, Solitons & Fractals, Elsevier, vol. 37(3), pages 817-826.
    2. Chen, Juhn-Horng, 2008. "Controlling chaos and chaotification in the Chen–Lee system by multiple time delays," Chaos, Solitons & Fractals, Elsevier, vol. 36(4), pages 843-852.
    3. Wang, Zhen & Hu, Weipeng, 2021. "Resonance analysis of a single-walled carbon nanotube," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).
    4. Marhl, Marko & Perc, Matjaž, 2006. "Determining the flexibility of regular and chaotic attractors," Chaos, Solitons & Fractals, Elsevier, vol. 28(3), pages 822-833.

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