Dynamical Systems: Equilibrium Points and Stability

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Introduction to Dynamical System

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

Numerical Analysis: Stability in ODEs

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

Dynamic Systems: Formalism and Bases

Covers the formalism and bases of dynamic systems, including differential equations and non-linear systems.

Small Scale Stability: Equilibrium Point

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

Equilibrium Points and Bifurcations

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

Concept of Stability in ODEs

Explores stability in ODEs, including error checks, equilibrium points, and global attractors, with a focus on numerical schemes like Euler's method.

Dynamics of Simple Pendulum and Lorenz Equations

Explores the dynamics of a simple pendulum and the intriguing Lorenz equations, highlighting sensitivity to initial conditions and the transition to chaos.

Bifurcations: Fold Bifurcation

Covers the concept of fold bifurcation in dynamical systems, focusing on the saddle-mode behavior.

Small Scale Stability: Gradient Systems

Explores small scale stability in gradient systems, analyzing trajectories and attractors in phase space.

Dynamical Systems: Maps and Stability

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