Delay Differential Equations: Methods and Practical Applications

Delay Differential Equations: Methods and Practical Applications

Presenter(s)

Amanda Maylath

Comments

1:15-2:30, Kennedy Union Ballroom

Description

Differential equations are essential in modeling systems in areas such as physics, biology, and engineering. This project explores delay differential equations (DDEs), a type of functional differential equation that builds on ordinary differential equations (ODEs) by including time delays. Incorporating delays allows for the rate of change or derivative to depend on the current state of the system and on its past states, making DDEs useful in modeling real-world systems where past states influence future outcomes. This project looks at several types of DDEs, including linear delay models, Hutchinson’s equation, and second-order delay equations. Solution methods include Laplace transforms and the method of steps in which traditional ODE techniques are applied, such as separation of variables, integrating factors, and variation of parameters. DDE solutions are compared with those of corresponding non-delayed models. Practical applications of DDEs include modeling population dynamics and analyzing engineering systems. These examples show the effectiveness of DDEs in providing a more accurate representation of real-world dynamical systems.

Publication Date

4-23-2025

Project Designation

Capstone Project

Primary Advisor

Sam J. Brensinger

Primary Advisor's Department

Mathematics

Keywords

Stander Symposium, College of Arts and Sciences

Institutional Learning Goals

Scholarship

Delay Differential Equations: Methods and Practical Applications

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