MAE 5790: Nonlinear Dynamics and Chaos
MAE 5790: Nonlinear Dynamics and Chaos (Spring 2014, Cornell University). Instructor: Professor Steven Strogatz. This course provides an introduction to nonlinear dynamics, with applications to physics, engineering, biology, and chemistry. It closely follows Prof. Strogatz's book, "Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and Engineering."
The mathematical treatment is friendly and informal, but still careful. Analytical methods, concrete examples, and geometric intuition are stressed. The theory is developed systematically, starting with first-order differential equations and their bifurcations, followed by phase plane analysis, limit cycles and their bifurcations, and culminating with the Lorenz equations, chaos, iterated maps, period doubling, renormalization, fractals, and strange attractors.
| Lecture 25 - Using Chaos to Send Secret Messages |
Lou Pecora and Tom Carroll's work on synchronized chaos. Proof of synchronization by He and Vaidya, using a Lyapunov function. Kevin Cuomo and Alan Oppenheim's approach to sending secret messages with chaos. Secure versus private communications. Anecdotes about Princess Diana, the early days of cell phones, Francis Ford Coppola's movie "The Conversation." Parameter modulation and signal masking. Demonstration of Cuomo's method for synchronizing Lorenz circuits and using them to send and receive private messages.
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