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Stochastic sensitivity of systems driven by colored noise

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  • Bashkirtseva, Irina

Abstract

We study a response of the general nonlinear dynamic system to the colored noise. A stochastic sensitivity analysis of equilibria forced by small exponentially-correlated Gaussian noise is carried out. For the stochastic sensitivity matrix of the equilibrium, a system of matrix equations is derived, and explicit solution is found in 2D case. Applying these theoretical results, we study a response of FitzHugh–Nagumo model to colored noise. We analyze how dispersion of random states near the deterministic equilibrium depends on the characteristic time of the power-limited colored noise. The effect of the colored-noise-induced excitability is discussed.

Suggested Citation

  • Bashkirtseva, Irina, 2018. "Stochastic sensitivity of systems driven by colored noise," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 505(C), pages 729-736.
    • Handle: RePEc:eee:phsmap:v:505:y:2018:i:c:p:729-736
    DOI: 10.1016/j.physa.2018.03.095
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    References listed on IDEAS

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    1. Goswami, Gurupada & Majee, Pradip & Kumar Ghosh, Pulak & Bag, Bidhan Chandra, 2007. "Colored multiplicative and additive non-Gaussian noise-driven dynamical system: Mean first passage time," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 374(2), pages 549-558.
    2. Guo, Qin & Sun, Zhongkui & Xu, Wei, 2016. "The properties of the anti-tumor model with coupling non-Gaussian noise and Gaussian colored noise," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 449(C), pages 43-52.
    3. Wang, Ke-Gang & Masoliver, Jaume, 1996. "Linear oscillators driven by Gaussian colored noise: crossovers and probability distributions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 231(4), pages 615-630.
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    Cited by:

    1. Han, Ping & Wang, Liang & Xu, Wei & Zhang, Hongxia & Ren, Zhicong, 2021. "The stochastic P-bifurcation analysis of the impact system via the most probable response," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).
    2. Lev Ryashko, 2023. "Analysis of Excitement Caused by Colored Noise in a Thermokinetic Model," Mathematics, MDPI, vol. 11(22), pages 1-11, November.

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