Random dynamics of the Morris-Lecar neural model.
Random dynamics of the Morris-Lecar neural model.
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DOI：
10.1063/1.1756118
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发表时间：
2004-06
期刊：
影响因子：
2.9
通讯作者：
T. Tateno;K. Pakdaman
中科院分区：
文献类型：
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作者：
T. Tateno;K. Pakdaman
确定神经元对类似于现实刺激的波动噪声输入的响应特性对于理解神经元编码是必不可少的。本研究针对这个问题，提供了一个随机动力系统分析的莫里斯-Lecar神经模型驱动的白色高斯噪声电流。根据参数的选择，确定性的莫里斯-勒卡模型可以被认为是一个典型的原型广泛遇到的类神经元膜，称为I类和II类膜。在这两个从兴奋到振荡制度的过渡与不同的分叉情况。这项工作探讨如何随机扰动影响这两个分叉的情况。首次数值计算表明，在白色高斯噪声电流驱动下的Morris-Lecar模型在相空间中具有唯一的平稳分布。数值计算还揭示了定量和定性的变化，在这种分布在附近的确定性系统的分叉。然而，尽管这些变化，我们的数值模拟表明，系统的李雅普诺夫指数保持在这些参数区域为负，表明没有动态随机分岔发生。此外，我们的数值模拟证实，无论确定性系统的渐近动力学，随机Morris-Lecar模型稳定在一个唯一的平稳随机过程。根据随机动力系统理论，我们的分析表明，加性噪声破坏了上述的分支序列，在莫里斯-Lecar模型的第一类和第二类政权的特征。这一结果的神经元编码方面的解释是，尽管在确定性动力学的I类和II类膜的差异，它们的响应噪声样刺激提出了一个可靠的功能。
Determining the response characteristics of neurons to fluctuating noise-like inputs similar to realistic stimuli is essential for understanding neuronal coding. This study addresses this issue by providing a random dynamical system analysis of the Morris-Lecar neural model driven by a white Gaussian noise current. Depending on parameter selections, the deterministic Morris-Lecar model can be considered as a canonical prototype for widely encountered classes of neuronal membranes, referred to as class I and class II membranes. In both the transitions from excitable to oscillating regimes are associated with different bifurcation scenarios. This work examines how random perturbations affect these two bifurcation scenarios. It is first numerically shown that the Morris-Lecar model driven by white Gaussian noise current tends to have a unique stationary distribution in the phase space. Numerical evaluations also reveal quantitative and qualitative changes in this distribution in the vicinity of the bifurcations of the deterministic system. However, these changes notwithstanding, our numerical simulations show that the Lyapunov exponents of the system remain negative in these parameter regions, indicating that no dynamical stochastic bifurcations take place. Moreover, our numerical simulations confirm that, regardless of the asymptotic dynamics of the deterministic system, the random Morris-Lecar model stabilizes at a unique stationary stochastic process. In terms of random dynamical system theory, our analysis shows that additive noise destroys the above-mentioned bifurcation sequences that characterize class I and class II regimes in the Morris-Lecar model. The interpretation of this result in terms of neuronal coding is that, despite the differences in the deterministic dynamics of class I and class II membranes, their responses to noise-like stimuli present a reliable feature.