Topics in Modern Dynamics

Modern dynamics is the idea that the same mathematical language, phase space, stability, and flow, describes systems that look nothing alike on the surface: firing neurons, oscillator networks, evolutionary games, microswimmers at low Reynolds number, and the physics engines inside video games. You'll move between analytical work on nonlinear and coupled systems and simulation-based exploration, with two midterms, two quizzes, and a final anchoring the theory side. It builds on a standard dynamics and differential equations background and is meant as a graduate-level survey that retools those tools for the systems people actually study now, across engineering, biology, and economics.