在許多生物物種例如鳥群、魚群以及細菌等所呈現出各種不同迷人的群體行為的吸引之下，我們試著使用自我推進粒子來模擬生物群體在二維空間中的行為。這些粒子受到自我驅動力的驅動之下在一個有阻力的環境中運動，並由於粒子之間的距離遠近不同,這些粒子彼此會產生互相吸引，排斥以及方向上的排列。在這篇論文中，我們主要著重在自我推進粒子在有限的空間中，在不同的驅動力的強度和範圍下所呈現出的狀態（相）。我們利用驅動力的強度及範圍的不同來建構我們的相圖，並且利用各個不同狀態的出現機率來定義相的邊界。此外，藉著觀察穩定狀態形成過程的動畫，我們假設了一個簡化的物理圖像來描述穩定有序狀態的形成過程，並且利用這個圖像來分析從無序至穩定有序狀態的形成機制。首先我們先試著找出形成時間與圖像關係，我們使用了兩個方法來決定且確認穩定狀態的形成時間，第一個方法是藉著在特徵速度上設定判斷標準來決定形成時間，第二個方法則是利用數值分析的方法找出序參數曲線的特徵值來決定形成時間。 Motivated by intriguing flocking behaviors of biological species such as birds, fish and bacteria, we present particle-based simulations for the flocking of self-propelling particles in two dimensional spaces. The particles are under self-propelling motion in a viscous environment. Depending on the inter-particle distance, they attract, repel and align their direction of motion with respect to each other. In this thesis, we focus on the phases for finite-size flocks at different amplitude and range of alignment force. We use amplitude and range of alignment force to construct the phase diagram, and define the phase boundary that separates vortex state from marching state is obtained by constructing the histogram for their appearances. Moreover, by observing the formation process using animations, we give a simplifying physical picture to describe the formation process for steady states, and use this picture to analyze mechanisms for formation times of such steady states from an nitially disordered state. In formation process, we use two methods to measure and confirm the results of formation time. First method use a threshold value on the history of characteristic velocity as our criteria, and second method use the numerical analysis for order parameter curve to measure the formation time.
