Chaos Theory: the language of (in)stability

Introduction to the concept of dynamical systems and their importance in predicting the behavior of complex systems like weather and planetary trajectories.

Explanation of chaotic deterministic systems where even small differences in initial conditions lead to vastly different outcomes, posing challenges in long-term prediction.

Discussion on autonomous differential equations and their representation in a Cartesian space, highlighting the uniqueness of trajectories and attractors in such systems.

Explanation of fixed point attractors and basin of attraction, using examples to demonstrate how certain points in a system act as attractors leading to predictable outcomes.

Overview of the Van der Pol attractor, its origin in electrical engineering, and the concept of limit cycle attractors with trajectories forming loops in phase space.

Introduction to the Lorenz attractor, its significance in chaos theory, and the concept of a strange attractor where trajectories never repeat and do not intersect.

Explanation of the predictability horizon in chaotic systems, the impact of initial errors on predictions, and the limitations in predicting complex systems like the Earth's atmosphere.

Reflecting on the beauty and uncertainty of predicting complex systems, drawing inspiration from the quote by Master Oogway about the present moment.