Nonlinear Dynamics: Stability and Chaos

Related lectures (31)

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Introduces equilibrium points and bifurcations in differential equations, discussing their stability and relevance in various contexts.

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

Explores stability analysis in linear systems, emphasizing eigenvalues, eigenvectors, and stable manifolds.

Introduces dynamical systems, equilibrium points, stability, vector fields, phase plots, and Lyapunov stability.

Explores stability in linear 2D systems, covering fixed points, vector fields, and phase portraits.

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

Covers the Newton method for finding zeros of functions using data interpolation.

Explores scaling and renormalization in statistical mechanics, emphasizing critical points and invariant properties.

Covers special types of systems, focusing on gradient systems and limit cycles, discussing equilibrium points, stability, and chaotic behavior.

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