Course Identification

Students are expected to have a background in linear algebra, differential equations, basic functional analysis, and some programming experience.

This course provides an introduction to the fundamental concepts of dynamical systems theory and chaos. Students will explore key ideas through simple model systems, utilizing discrete maps and ordinary differential equations. The course will highlight how these models arise in various fields, particularly in physics and biology, providing real-world context for the theoretical concepts. The goal is to equip students with analytical tools, practical methods, and geometrical intuition to confidently analyze and solve problems involving low dimensional nonlinear dynamical systems.

Depending on student background, interest, and input, there will be opportunities to explore the integration of machine learning tools and techniques, such as neural networks and data-driven modeling, to complement the classical analysis of dynamical systems.

Students will be able to analyze and solve both linear and nonlinear dynamical systems, applying stability analysis, bifurcation theory, and chaos theory to real-world physical and biological models. When the underlying dynamics is low dimensional, they will develop geometrical intuition for interpreting system behavior using phase space analysis. Additionally, students will gain practical experience in using numerical methods and machine learning tools to simulate, predict, and analyze complex dynamical systems. They will be able to integrate classical dynamical systems theory with modern computational techniques, preparing them to approach high-dimensional, nonlinear, and chaotic systems in a variety of scientific fields