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在神经系统中，脑疾病的发生往往对应着神经系统的临界转迁与神经元的异常放电，因此对临界转迁的早期预警信号（EWS）的研究有助于预测神经元的放电行为，从而预防脑疾病的发生．传统EWS，如自相关系数、方差等指标，虽然能对动力系统的分岔点进行早期预警，但其无法对分岔类型进行区分．而基于功率谱的EWS可以有效预测分岔点并且区分分岔类型，且在气候及生态模型上的预测效果良好．本文将基于功率谱的EWS应用在神经元系统中，先后考察了Morris-Lecar和Hindmarsh-Rose模型神经元放电所对应的四种余维一分岔点前的临界现象，分别计算了传统EWS和基于功率谱的EWS，并进行了对比分析．结果表明基于功率谱的EWS能有效地预测神经元放电，并且能够对不同神经元的I型兴奋和II型兴奋作出区分．本研究对神经系统的临界转迁的预测有着重要的指导意义，对神经系统疾病的诊断和治疗有着重要的启示作用．Brain diseases often coincide with critical transitions in neural system and abnormal neuronal firing. Studying early warning signals (EWS) of critical transitions can offer a promising avenue for predicting neuronal firing behaviors, which can potentially aid in the early diagnosis and prevention of brain diseases. Conventional EWS, such as autocorrelation and variance, have been widely used to detect the critical transitions in various dynamical systems. However, these methods are limited in distinguishing different types of bifurcations. In contrast, EWS with power spectrum have shown a significant advantage in not only predicting bifurcation points but also distinguishing the types of bifurcations involved. Previous studies have demonstrated its predictive power in climate and ecological models. Based on this, this study applies the EWS with power spectrum to neuronal systems in order to predict the neuronal firing behaviors and distinguish different classes of neuronal excitability. Specifically, we compute the EWS before the occurrence of saddle-node bifurcation on the invariant circle and subcritical Hopf bifurcation in the Morris-Lecar neuron model. Additionally, we extend the analysis to the Hindmarsh-Rose model, calculating EWS before both saddle-node bifurcation and supercritical Hopf bifurcation. The study contains the four types of codimension-1 bifurcations corresponding to the neuronal firing. For comparison, we also calculate two types of conventional EWS: lag-1 autocorrelation and variance. In numerical simulations, the stochastic differential equations are simulated by the Euler-Maruyama method. Then, the simulated responses are detrended by the Lowess filter. Finally, the EWS are calculated using the rolling window method to ensure the detection of EWS before bifurcation points. Our results show that the EWS with power spectrum can effectively predict the bifurcation points, which mean that it can predict neuronal firing activities. Comparing with the lag-1 autocorrelation and the variance, the EWS with power spectrum not only accurately predict the neuronal firing, but also distinguish the classes of excitability in neurons. That is, according to the different characteristics of the power spectrum frequencies, the EWS with power spectrum can effectively distinguish saddle-node bifurcations and Hopf bifurcations during neuronal firing. This work presents a novel approach for predicting the critical transitions in neural system, with potential applications in diagnosing and treating brain diseases.
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Keywords:
- neurodynamics /
- power spectrum /
- critical transitions /
- early warning signals
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[1] Grziwotz F, Chang C W, Dakos V, van Nes E H, Schwarzländer M, Kamps O, Heßler M, Tokuda I T, Telschow A, Hsieh C H 2023 Sci. Adv. 9 eabq4558
[2] Strogatz S H 2018 Nonlinear dynamics and chaos: with applications to physics, biology, chemistry, and engineering (Boca Raton: CRC press) pp70-80
[3] Maturana M I, Meisel C, Dell K, Karoly P J, D’Souza W, Grayden D B, Burkitt A N, Jiruska P, Kudlacek J, Hlinka J, Cook M J, Kuhlmann L, Freestone D R 2020 Nat. Commun. 11 2172
[4] Dakos V, Carpenter S R, Brock W A, Ellison A M, Guttal V, Ives A R, Kéfi S, Livina V, Seekell D A, van Nes E H 2012 PLoS One 7 e41010
[5] Carpenter S R, Brock W A 2006 Ecol. Lett. 9 311
[6] Held H, Kleinen T 2004 Geophys. Res. Lett. 31 L23207
[7] Boettiger C, Hastings A 2012 J. R. Soc. Interface. 9 2527
[8] Scheffer M, Bascompte J, Brock W A, Brovkin V, Carpenter S R, Dakos V, Held H, van Nes E H, Rietkerk M, Sugihara G 2009 Nature 461 53
[9] Lade S J, Gross T 2012 PLoS Comput. Biol. 8 e1002360
[10] Carpenter S R, Brock W A 2011 Ecology 92 2196
[11] Bauch C T, Sigdel R, Pharaon J, Anand M 2016 Proc. Natl. Acad. Sci. U. S. A. 113 14560
[12] Yan P C, Hou W, Hu J G 2012 Acta Phys. Sin. 61 543 (in Chinese) [颜鹏程, 侯威, 胡经国, 2012 物理学报 61 543]
[13] Wu H, Hou W, Yan P C 2013 Acta Phys. Sin. 62 548 (in Chinese) [吴浩, 侯威, 颜鹏程 2013 物理学报 62 548]
[14] Wu H, Hou W, Yan P C, Feng G L 2013 Acta Phys. Sin. 61 561 (in Chinese) [吴浩, 侯威, 颜鹏程, 封国林 2012 物理学报 61 561]
[15] Boers N 2018 Nat. Commun. 9 2556
[16] Meisel C, Klaus A, Kuehn C, Plenz D 2015 PLoS Comput. Biol 11 e1004097
[17] Dakos V, Van Nes E H, D’Odorico P, Scheffer M 2012 Ecology 93 264
[18] Kuznetsov Y A 2023 Elements of Applied Bifurcation Theory (Cham: Springer International Publishing) pp77-102
[19] Bury T M, Bauch C T, Anand M 2020 J. R. Soc. Interface. 17 20200482
[20] Chen Z, Fan P Y, Hou X T, Feng G L, Qian Z H 2024 Chaos Solitons Fractals 187 115409
[21] Gardiner C W 1985 Handbook of stochastic methods for physics, chemistry and the natural sciences (Berlin: Springer) pp:106-107
[22] Box G E, Jenkins G M, Reinsel G C, Ljung G M 2015 Time series analysis: forecasting and control (Hoboken: John Wiley & Sons) pp21-47
[23] Welch P 1967 IEEE Trans. Audio Electroacoustics 15 70
[24] Prescott S A, De Koninck Y, Sejnowski T J 2008 PLoS Comput. Biol 4 e1000198
[25] Liu C M, Liu X L, Liu S Q 2014 Biol. Cybern. 108 75
[26] Kendall M G 1938 Biometrika 30 81
[27] Lv M, Wang C N, Ren G D, Ma J, Song X L 2016 Nonlinear Dyn. 85 1479
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