在複雜系統中有一典型的特色就是難以建模，其原因來自系統本身的高自由
度或系統與環境的交互作用所致。在本論文中，我們討論了複雜系統中的兩種不同類型的 一維的動力學。
第一個主題是關於 機械敏感黏附複合物、肌球蛋白馬達和肌動蛋白網絡分佈之間的相互作用所產生的單一細胞的一維軌跡。 我們的活性凝膠模型中的所有方程式都是決定性的，即方程式中沒有任何的隨機性。當黏附複合物的機械敏感性較弱且肌球蛋白的收縮性夠強時， 細胞以恆定速度移動。此外，具有高度機械敏感性黏附複合物的細胞隨著肌 球蛋白收縮性增加，呈現出週期性的往復運動。基於活性凝膠模型提出一個簡化模型解釋了這些運動行為轉變背後的機制。
第二個主題是固體摩擦中黏滑動力學的統計，在實驗中，一次的黏滑事件可以由三個物理量來表徵，這些物理量的統計顯示出某些普遍行為，本論文提出了一個基於實驗數據的新模型。在這個題目中，兩個固體之間的接觸面是隨機的，因此系統的運動方程式不是確定性的。透過建構力場來 呈現 表面隨機性的效應，當兩個位置間的距離小於特徵長度 (????)，力場的相關函數是布朗相關的，當距離超過????時，它會飽和。我們的模型再現了關鍵物理量的統計，包括表面等效彈性常數的指數分佈、引發滑動的臨界力的廣義極值分佈以及滑動事件期間釋放的力（滑動長度）的冪律分佈。我們構建的力場幫助我們理解 黏 滑動力學的普遍特性和非普遍特性的起源。;A typical character of complex systems is the difficulty in modeling due to the complicated relations arising from the degrees of freedom of the system or the interplay between the environment and the system. In this \emph{thesis}, we discuss two different types of one-dimensional dynamics in complex systems.
The first topic is the one-dimensional trajectories of a single cell resulting from the interplay between the distributions of mechanosensitive adhesion complexes, myosin motors, and actin network.
All the equations in our active gel model are deterministic, that is, there is no randomness in the equations.
It is found that when the mechanosensitivity of adhesion complexes is weak, the cell moves at a constant velocity as the myosin contractility is sufficiently large.
Furthermore, a cell with highly mechanosensitive adhesion complexes exhibits periodic back-and-forth motion as the myosin contractility increases.
Based on the active gel model, a simplified model is presented to show the mechanisms behind the transitions between these motility behaviors.
The second topic is the statistics of the stick-slip dynamics in solid friction.
In the experiment, a stick-slip event can be characterized by three physical quantities, and their statistics exhibit certain universal behaviors.
This {\it thesis} reports a new model based on the experimental data.
In this case, the contact surface between the two solid is random, therefore the equation of motion of the system is not deterministic.
A force landscape is constructed to represent the effect of surface randomness.
The correlation function of the force landscape is Brownian correlated when the distance between two positions is less than a characteristic length $l_d$, and it saturates when the distance is beyond $l_d$.
Our model reproduces the statistics of the key physical quantities including the exponential distribution of the effective elastic constants of the surface, the generalized extreme value distribution for the critical force beyond which slips are initiated, and the power-law distribution of the force drop (slip length) during the slip events.
The force landscape we constructed helps us understand the origin of the universal and non-universal characteristics of stick-slip dynamics.
