BE 500: Introduction to Differential Equations for Bioengineers - Lecture 09

BE 500: Introduction to Differential Equations for Bioengineers (Summer 2025)

This lecture focuses extensively on stability analysis, a crucial concept for understanding dynamic systems in bioengineering. It begins by defining stability and explaining its importance in biological systems, which are inherently nonlinear. The lecture covers different types of stability, including local, global, and asymptotic stability, and introduces tools like linear stability analysis, Lyapunov functions, and basin of attraction. Key applications in bioengineering are discussed, such as gene regulatory networks, neural dynamics, and population models. The lecture provides detailed examples using the logistic growth model, Hill equation, and Lotka-Volterra equations to demonstrate stability analysis techniques. It also explores the limitations of linear stability analysis and the challenges of working with nonlinear systems, emphasizing the need for multiple approaches to fully understand system behavior. Throughout, the lecture highlights the importance of stability analysis in predicting long-term behavior and designing robust biological systems.

Codes can be accessed using: https://github.com/HossamBalaha/BE-50...

Playlist from Summer 2025:    • BE 500: Introduction to Differential Equat...