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Stochastic sensitivity analysis of noise-induced intermittency and transition to chaos in one-dimensional discrete-time systems


  • Bashkirtseva, Irina
  • Ryashko, Lev


We study a phenomenon of noise-induced intermittency for the stochastically forced one-dimensional discrete-time system near tangent bifurcation. In a subcritical zone, where the deterministic system has a single stable equilibrium, even small noises generate large-amplitude chaotic oscillations and intermittency. We show that this phenomenon can be explained by a high stochastic sensitivity of this equilibrium. For the analysis of this system, we suggest a constructive method based on stochastic sensitivity functions and confidence intervals technique. An explicit formula for the value of the noise intensity threshold corresponding to the onset of noise-induced intermittency is found. On the basis of our approach, a parametrical diagram of different stochastic regimes of intermittency and asymptotics are given.

Suggested Citation

  • Bashkirtseva, Irina & Ryashko, Lev, 2013. "Stochastic sensitivity analysis of noise-induced intermittency and transition to chaos in one-dimensional discrete-time systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(2), pages 295-306.
  • Handle: RePEc:eee:phsmap:v:392:y:2013:i:2:p:295-306
    DOI: 10.1016/j.physa.2012.09.001

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    References listed on IDEAS

    1. Bashkirtseva, I.A & Ryashko, L.B, 2000. "Sensitivity analysis of the stochastically and periodically forced Brusselator," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 278(1), pages 126-139.
    2. Ryashko, L. & Bashkirtseva, I. & Gubkin, A. & Stikhin, P., 2009. "Confidence tori in the analysis of stochastic 3D-cycles," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 80(2), pages 256-269.
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    Cited by:

    1. Bashkirtseva, Irina & Ryashko, Lev, 2017. "Stochastic sensitivity analysis of noise-induced order-chaos transitions in discrete-time systems with tangent and crisis bifurcations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 467(C), pages 573-584.
    2. repec:eee:thpobi:v:115:y:2017:i:c:p:61-68 is not listed on IDEAS
    3. Irina Bashkirtseva & Alexander Pisarchik & Lev Ryashko & Tatyana Ryazanova, 2016. "Excitability And Complex Mixed-Mode Oscillations In Stochastic Business Cycle Model," Advances in Complex Systems (ACS), World Scientific Publishing Co. Pte. Ltd., vol. 19(01n02), pages 1-16, February.


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