Lecture

Nonlinear Dynamics: Stability and Chaos

Related lectures (31)

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

Dynamical Systems: Maps and Stability

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

Stability Analysis: Linear Systems

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

Introduction to Dynamical System

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

Linear Systems in 2D: Stability

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

Introduction to Quantum Chaos

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

Newton Method: Data Interpolation

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

Scaling & Renormalization in Statistical Mechanics

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

Special Types of Systems: Limit Cycles

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

Synchronization in Kuramoto Model

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

Nonlinear Dynamics and Complex Systems

Covers chaotic behavior in complex systems, with applications in various fields and a historical overview of major developments in chaos theory.

Dynamical Systems for Engineers

Covers the theoretical basis of linear and nonlinear dynamical systems for engineers.

Nonlinear Equations: Fixed Point Method Convergence

Covers the convergence of fixed point methods for nonlinear equations, including global and local convergence theorems and the order of convergence.

Dynamic Systems: Formalism and Bases

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

Nonlinear Dynamics and Chaos

Explores logistic maps, bifurcations, equilibrium points, and periodic orbits in nonlinear dynamics and chaos.

Nonlinear Equations: Fixed Point Method

Covers the topic of nonlinear equations and the fixed point method.

Stability of ODE

Explores the stability of Ordinary Differential Equations, focusing on solution dependence, critical data, linearization, and control of nonlinear systems.

Discrete Time Solution: Stability Properties and Fixed Points

Explores stability properties and fixed points in discrete time solutions.

Dynamic Systems: Course Review

Covers dynamic systems, trajectories, growth models, stability of fixed points, and linearization of models.

Fixed Points and Stability

Explores fixed points and their stability in dynamic systems, emphasizing linear stability analysis.