Collective Behavior of Particles Whose Dynamics is Governed by Brownian Agent

The model is an existing or mentally represented object, which in the process of studying replaces real phenomenon. It is considered, the process of the random walk in this paper. To further research, it is necessary to make it possible for the model to acquire new knowledge about studied phenomenon, it allows us to predict its future development and indicate the direction of improvement. In this paper deals with several models of a random walk on a one-dimensional grid. There are exist agent and particle in the first model. Agent walks randomly with the same probability of making right or left steps. When the agent meets with the particle, he can push it by a certain distance from 0 to (m-1). In the second model, it is considered two of such particles and one agent, which can govern them. In the third model, there are two agents and two particles. In of these particles is controlled by each agent. Studied trajectories of agent and particle, distribution of the beer can's final coordinates and the curves of the standard deviation over time. In the tasks, where the two particles exists the standard deviation were taken as the distance between the two banks. The purpose of this master's thesis is to develop and implement algorithms model of a random walk on a one-dimensional grid, and to compare and analyze the mentioned tasks among themselves.