Two types of noise induced oscillations (NIOs) near Hopf bifurcation and coherence resonance (CR) have been studied analytically in a calcium system. One is NIOs with small amplitude and internal signal stochastic resonance (CR type I) occurs, and the other is noise induced spike and the regularity of which reaches a maximum at an optimal noise level (CR type II). For the first type, stochastic normal form theory is employed to analyze the signal to noise ratio of the NIOs depending on the noise intensity. For the second type, based on the independent assumption, activation time and excursion time have been split, and the sum of which reach a minimum with the variation of noise intensity. The theoretical evidence is also explained in detail. Numerical simulations show good agreements with the theoretical results. It may indicate some kind of transmit mechanism involved in stochastic calcium dynamics.

中文翻译：

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细胞内钙振荡系统中的两种相干共振

在钙系统中，已经分析研究了Hopf分叉附近的两种类型的噪声感应振荡（NIO）和相干共振（CR）。一个是幅度较小的NIO，并且会发生内部信号随机共振（CR类型I），另一个是噪声引起的尖峰信号，其规律性在最佳噪声水平下达到最大值（CR类型II）。对于第一类，采用随机范式理论来分析NIO的信噪比，具体取决于噪声强度。对于第二种类型，基于独立的假设，已将激活时间和偏移时间分开，并且它们的总和随着噪声强度的变化达到最小值。理论证据也进行了详细说明。数值模拟表明与理论结果吻合良好。