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Determining the flexibility of regular and chaotic attractors

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  • Marhl, Marko
  • Perc, Matjaž

Abstract

We present an overview of measures that are appropriate for determining the flexibility of regular and chaotic attractors. In particular, we focus on those system properties that constitute its responses to external perturbations. We deploy a systematic approach, first introducing the simplest measure given by the local divergence of the system along the attractor, and then develop more rigorous mathematical tools for estimating the flexibility of the system’s dynamics. The presented measures are tested on the regular Brusselator and chaotic Hindmarsh–Rose model of an excitable neuron with equal success, thus indicating the overall effectiveness and wide applicability range of the proposed theory. Since responses of dynamical systems to external signals are crucial in several scientific disciplines, and especially in natural sciences, we discuss several important aspects and biological implications of obtained results.

Suggested Citation

  • Marhl, Marko & Perc, Matjaž, 2006. "Determining the flexibility of regular and chaotic attractors," Chaos, Solitons & Fractals, Elsevier, vol. 28(3), pages 822-833.
    • Handle: RePEc:eee:chsofr:v:28:y:2006:i:3:p:822-833
    DOI: 10.1016/j.chaos.2005.08.013
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    References listed on IDEAS

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    1. Perc, Matjaž & Marhl, Marko, 2004. "Frequency dependent stochastic resonance in a model for intracellular Ca2+ oscillations can be explained by local divergence," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 332(C), pages 123-140.
    2. 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.
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    Cited by:

    1. 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.
    2. Khajanchi, Subhas & Ghosh, Dibakar, 2015. "The combined effects of optimal control in cancer remission," Applied Mathematics and Computation, Elsevier, vol. 271(C), pages 375-388.
    3. 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.

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