Lyapunov Stability: Theory and Applications

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Explores Lyapunov stability and invariance of dynamical systems through examples and corollaries.

Explores one-dimensional maps, periodic solutions, and bifurcations in dynamical systems.

Explores the Kuramoto model for synchronization in phase oscillators and discusses stability criteria and critical coupling values.

Covers the introduction to Quantum Chaos, classical chaos, sensitivity to initial conditions, ergodicity, and Lyapunov exponents.

Covers exercises on the Lyapunov method in non-linear control systems, focusing on stability analysis and Lyapunov functions.

Explores fixed point stability, Lyapunov functions, Lotka-Volterra models, and nonlinear dynamics in complex systems.

Covers the stability analysis of ODEs using numerical methods and discusses stability conditions.

Covers small scale stability at equilibrium points in dynamical systems for engineers.

Explores Chaos Theory through Discrete Dynamical Systems and the Arnold's Cat Map.

Explores stability and eigenvalues of LTI systems, reachability, and controllability of dynamical systems.