本研究著重探討頻率編碼中的常用的分析工具——觸發頻率函數（firing rate function）。我們採用平衡背景雜訊的 Leaky Integrate-and Fire（BLIF）神經元模型，來模擬生物神經元在自然生物體內環境中的行為，並研究週期性輸入信號對於觸發頻率的影響。我們提出假設以解釋觸發頻率相位偏移現象的機制，並透過系統性模擬，來探討輸入頻率與背景雜訊的調控對此現象的影響。本研究中提出了創新的神經元靈敏度分數（AG score）概念，並提供數種神經元模型的對應計分公式，為各種神經元模型間之互相比較提供量化依據；靈敏度分數也能夠作為神經網路建構時，欲替換不同類型神經元的參考。除此之外，本文還分析了 Izhikevich 神經元模型的動態特性，將其微分方程描述為速度向量場，並且依此推導出對應的 Hamiltonian 能量函數以研究神經訊號觸發間隔（ISI）之觸發頻率。研究發現在平衡背景雜訊的 Izhikevich 神經元模型中，ISI 觸發頻率曲線出現相位提前現象，顯示輸出信號領先於輸入信號，為相位偏移的機制提供了新的見解。本研究結果為觸發頻率函數的應用提供了新啟示，並
揭示了背景雜訊與輸入頻率在神經元編碼機制調控中的關鍵作用。

This study focuses on the analysis of firing rate function, a commonly used tool in rate coding research. Using the Balanced Leaky Integrate-and-Fire (BLIF) model, we simulated the behavior of biological neurons in vivo and investigated the effects of periodic input signals on firing rates. Hypotheses were proposed to explain the mechanisms underlying phase shifts in firing rates, and systematic simulations were conducted to explore the influence of input frequency and background noise regulation on this phenomenon. In this study we introduce the innovative concept of the agility score (AG score) for a neuron model and provide corresponding scoring equations for several neuron models, offering a quantitative basis for comparisons among various neuron models. The AG score can also serve as a reference for substituting different types of neurons during the construction of neural networks. Additionally, the dynamic properties of the Izhikevich model were analyzed by representing its differential equations as a velocity field. The associated Hamiltonian energy function was derived to study the interspike interval (ISI) firing rate. A phase advance phenomenon was observed in the ISI firing rate curve of a balanced Izhikevich neuron model, where the output signal leads the input signal, providing new insights into the mechanisms of phase shifts. These findings contribute to a deeper understanding of
firing rate function applications and highlight the critical roles of background noise and input frequency in regulating neuronal coding mechanisms.

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