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<p>We study how to predict bifurcation points in continuous dynamical systems, with a particular focus on complex behaviors relevant to neuroscience. Standard early warning signals such as autocorrelation, variance, skewness, and kurtosis work well for simple bifurcations but often fail for transitions involving limit cycles, period-doubling, or chaos. Building on our earlier work with discrete maps, we adapt the period-based decomposition method to continuous flows. Our approach first samples the dynamics with a Poincaré section, then estimates the dominant period and decomposes the signal into sub-series. Early warning indicators are computed for each sub-series and averaged to produce modified signals. Applying this method to the Hindmarsh-Rose neuron model, we show that the modified indicators reveal clear and consistent trends before period-doubling and chaotic transitions, greatly improving on standard approaches. We also find that focusing on the slowest system variable is essential for obtaining reliable signals. Our results indicate that this framework provides a powerful tool for anticipating complex critical transitions in continuous dynamical systems and may help predict challenging dynamics in real-world settings.</p>

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Predicting bifurcation points in continuous chaotic neuron models

  • 期刊论文

  • 发表日期：

    2025年12月5日

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  • Shivakumar Rajagopal,
  • Fahimeh Nazarimehr,
  • Karthikeyan Rajagopal,
  • Sajad Jafari,
  • Matjaž Perc

摘要

We study how to predict bifurcation points in continuous dynamical systems, with a particular focus on complex behaviors relevant to neuroscience. Standard early warning signals such as autocorrelation, variance, skewness, and kurtosis work well for simple bifurcations but often fail for transitions involving limit cycles, period-doubling, or chaos. Building on our earlier work with discrete maps, we adapt the period-based decomposition method to continuous flows. Our approach first samples the dynamics with a Poincaré section, then estimates the dominant period and decomposes the signal into sub-series. Early warning indicators are computed for each sub-series and averaged to produce modified signals. Applying this method to the Hindmarsh-Rose neuron model, we show that the modified indicators reveal clear and consistent trends before period-doubling and chaotic transitions, greatly improving on standard approaches. We also find that focusing on the slowest system variable is essential for obtaining reliable signals. Our results indicate that this framework provides a powerful tool for anticipating complex critical transitions in continuous dynamical systems and may help predict challenging dynamics in real-world settings.