## Honors College Theses

### Math Modeling and Simulation of a Chasing Game

11-2-2022

#### Major

Mathematics (B.S.)

#### Document Type and Release Option

Thesis (restricted to Georgia Southern)

Dr. Yan Wu

#### Abstract

This study is based on a chasing game between two objects, one being a chaser and the other a moving target. For this problem, we assume that the chaser is always moving in a direction such that it is in line with the target. To put that assumption into a mathematical model, we used a system of differential equations to map the trajectory of the chaser. We used the fourth order Runge-Kutta method, a highly accurate method of solving ordinary differential equations, to solve these equations numerically. The goal of this project is to develop a mathematical model to precisely predict the trajectory of the chaser as it moves toward the target. We will use this model to find the minimum speed of the chaser at a specified target speed with three other fixed parameters: target path, initial position of the chaser, and a vertical boundary. We hope to identify the impact of different system parameters on the outcome of the chasing game. This problem can be further worked on to predict minimum speeds in various chasing scenarios and could potentially be linked to the design of tactical guided missiles.

#### Thesis Summary

Chasing games are all around us. These interactions plague our everyday life and be observed and predicted using mathematical modeling. For this project, we did just that, with a bunny being the target and a dog being the chaser. By using a system of ordinary differential equations solved using the Runge-Kutta method, we were able to observe and better understand these games. We first put the concept into a program using the software MATLAB. This was essential since the ordinary differential equations we used to map the trajectory of the dog were unable to be solved by hand. We then used this program to answer a series of what if questions, such as if the bunny goes this fast, how fast must the dog go to catch it? We concluded that there is a scenario in which both entities win and that there is a way to find the minimum speed the dog must travel to win.

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