神經生理學家Donald O. Hebb所提出的細胞集合學說，描述了大腦的神經線路可透過突觸的可塑性機制來產生自我持續的反射性活躍，並藉此產生相關區域神經元之間結構上的交互連結，以建構出腦內資訊表現的基本砌塊。在神經生理學上，已有越來越多的實驗證據支持Hebb的細胞集合學說，也因此促使了大量以突觸的可塑性機制為基礎的計算機及複雜網路模型的建立。透過這些模型的建立，同時引發了一個更深層的數學或生物上的問題：為何突觸的可塑性機制所蘊含的神經元群體之間隨時間與神經元活躍狀態相應變化的交互作用，能夠在細胞集合成長的動力過程中扮演著關鍵的角色? 藉由模型化神經元群體的自我組織動力行為，我們從中量化了兩種形態的可演化量，並發展出脈衝動力學的概念。從這兩種形態的可演化量所推導出的脈衝動力學定律，使得我們可數學地證明了在一個模擬腦神經元運作的高維度的交互連結自我組織系統中，因其可塑性而不斷變化且交互影響的可演化網路節點與耦合動力行為，最終可達到群體神經元的活躍同步化，並在此活躍同步化期間與相應產生的突觸增強作用形成了正回饋效應，藉此正回饋效應，群體神經元之間將可產生與活躍同步化相關的神經迴路。這個可演化的網路模型不但可詮釋出腦內複雜系統運作的動力方程，並且對Hebb所提出的細胞集合學說提供了一個精確的數學解釋。

Donald O. Hebb's neurophysiological cell-assembly postulate provides the first description of a mechanism for synaptic plasticity by which cortical circuits might admit self-sustaining reverberatory activity to bind association-area neurons into the basic building blocks of information. There is increasing empirical support for Hebb's contribution to neuropsychological theory and there also stimulates an intensive effort to promote the building of computer or network models of the brain based on Hebbian synaptic plasticity. And that raises a profound mathematical or biological question: Why do those time- and activity-dependent interactions underlying plasticity allow neural populations to capture the characteristic property of the entire ensembles of cell assemblies? By modeling the neuronal ensemble dynamics of assembly organization, we quantify two evolutionary quantities that originate the concept of pulsedynamics, and with them come a formulation of a dynamical-combinatorial process in a huge, interconnected self-organizing system, in which the ongoing changes of the nodal-and-coupling dynamics underlying plasticity are guaranteed to result in group synchrony and sync-dependent circuits. This evolutionary network model
serves to describe dynamic equations of the complex brain system and leads to a mathematical explanation for the mystery of the growth of cell assemblies.

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