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Adaptive synchronization in excitable neuron ensemble under Lévy noise

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  • Ramazanov, Ibadulla R.
  • Bukh, Andrei V.
  • Shepelev, Igor A.

Abstract

We study the effect of Lévy noise on phase synchronization in adaptive ensembles of excitable elements. We consider an ensemble of FitzHugh–Nagumo neurons with nonlocal coupling and a ring topology, under the external additive α-stable Lévy noise. A key feature of the model is the adaptive coupling tuning mechanism, which adjusts the strength of interactions between neurons based on a moving average of the interspike interval. The coupling strength increases during spikes with a large interspike interval and decreases during synchronous spikes, which allows the network to automatically adjust the minimum necessary total coupling strength to maintain a coherent regime even under strong noise with heavy distribution tails. We found that the coherent resonance characteristic of a single neuron is also observed in a coupled system. However, the optimal noise intensity shifts to lower values as the coupling range increases. Synchronization is achieved only at a certain coupling range, while at a lower coupling range only cluster synchronization is possible even with strong coupling of neurons. Lévy noise requires a stronger global interaction between neurons to achieve synchronization compared to Gaussian noise. However, the positive asymmetry of the noise distribution significantly reduces this threshold due to the increased sensitivity of neurons to positive fluctuations. The proposed adaptive mechanism successfully ensures synchronization of the system in the entire studied range of Lévy noise parameters and connection topology, demonstrating the versatility, high adaptation speed and energy efficiency of the approach. The obtained results open up new possibilities for controlled coordination of spatiotemporal dynamics in neural and other nonlinear excitable systems under extreme stochastic influences.

Suggested Citation

  • Ramazanov, Ibadulla R. & Bukh, Andrei V. & Shepelev, Igor A., 2025. "Adaptive synchronization in excitable neuron ensemble under Lévy noise," Chaos, Solitons & Fractals, Elsevier, vol. 201(P1).
    • Handle: RePEc:eee:chsofr:v:201:y:2025:i:p1:s0960077925012032
    DOI: 10.1016/j.chaos.2025.117190
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    References listed on IDEAS

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    1. Rybalova, E.V. & Vadivasova, T.E. & Strelkova, G.I. & Zakharova, A., 2022. "Multiplexing noise induces synchronization in multilayer networks," Chaos, Solitons & Fractals, Elsevier, vol. 163(C).
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    3. Korneev, Ivan & Zakharova, Anna & Semenov, Vladimir V., 2024. "Lévy noise-induced coherence resonance: Numerical study versus experiment," Chaos, Solitons & Fractals, Elsevier, vol. 184(C).
    4. Weron, Rafal, 1996. "On the Chambers-Mallows-Stuck method for simulating skewed stable random variables," Statistics & Probability Letters, Elsevier, vol. 28(2), pages 165-171, June.
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