Nonlinear Dynamics and Complex Systems

This lecture introduces the study of complex systems, characterized by chaotic behavior, extreme sensitivity to initial conditions, fractal geometry, and self-organized criticality. These systems exhibit multiple metastable states and a non-Gaussian distribution of outputs, making long-term predictions impossible. The course covers techniques to analyze nonlinear and complex systems, with applications in various fields like social systems, biology, and climate. The history of chaotic systems is discussed, from Poincaré's non-linear solutions to Lorenz's unpredictable system. Major developments in chaos theory, such as the explanation of turbulence onset and the discovery of universal laws in chaos, are also explored.