Nonlinear Dynamics: Stability and Chaos

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Chaos and Lyapunov Exponents: Analyzing Predictability

Covers Lyapunov exponents, chaos measurement, and perturbation analysis in dynamical systems.

Newton's Method: Convergence and Criteria

Explores the Newton method for non-linear equations, discussing convergence criteria and stopping conditions.

Circle Criterion: Stability and Nonlinearity

Covers the concept of passivity in linear systems and the circle criterion for absolute stability.

Small Scale Stability

Covers small scale stability conditions and asymptotic behavior around fixed points.

Stability of LTI Systems: Equilibria and Lyapunov Theory

Covers equilibria, stability analysis, and Lyapunov theory in linear systems, focusing on eigenvalues and stability properties.

Learning and Adaptive Control for Robots: SEDS & LPV-DS

Explores learning and adaptive control for robots through SEDS and LPV-DS, emphasizing stability, non-linear dynamics, and optimization.

Numerical Analysis: Nonlinear Equations

Explores the numerical analysis of nonlinear equations, focusing on convergence criteria and methods like bisection and fixed-point iteration.

Quantum Chaos and Scrambling

Explores the concept of scrambling in quantum chaotic systems, connecting classical chaos to quantum chaos and emphasizing sensitivity to initial conditions.

Introduction to Nonlinear Systems Control

Covers the analysis and control of nonlinear systems, including methods like phase plan and passivity.

Dynamical Systems: Equilibrium Points and Stability

Covers dynamical systems, equilibrium points, stability analysis, and phase plots using examples like the pendulum system.