Nonlinear Systems Courses and Certifications

IIT Kharagpur;  NPTEL

Advanced Theory of Ordinary Differential Equations

Comprehensive exploration of advanced ODE theory, covering existence, stability, chaos, perturbations, bifurcations, and applications in mechanical and electrical systems. Includes mathematical modeling and solution techniques.

• Swayam
• 12 weeks
• On-Demand
• Free Online Course

Power Electronics: State Space Averaging and Linearization - Lecture 25

Explore state space averaging for modeling switching converters and linearization of nonlinear averaged models to realize control-to-output transfer functions in power electronics.

• YouTube
• 51 minutes
• On-Demand
• Free Video

Beijing Jiaotong University

Nonlinear Dynamical System and Application

Master advanced concepts in nonlinear dynamical systems, from stability and bifurcations to chaos theory, with practical applications in natural sciences, social sciences, and engineering.

• XuetangX
• On-Demand
• Free Online Course

IIT Delhi;  NPTEL

Nonlinear and Adaptive Control

Explore advanced control system design, focusing on adaptive control for systems with parametric uncertainty. Develop skills in controller design using Lyapunov Stability Theory and MATLAB/Simulink.

• Swayam
• 4 weeks
• On-Demand
• Free Online Course

Complexity Academy

Complexity Theory an Introduction

Explore core concepts of complex systems theory, including systems theory, nonlinear systems, network theory, and adaptive systems, to gain fresh perspectives on financial systems, environment, and social organizations.

• Independent
• On-Demand
• Free Online Course

Steve Brunton

Drawing Phase Portraits for Nonlinear Systems

Learn to analyze nonlinear systems by drawing phase portraits, identifying fixed points, linearizing, and inferring global dynamics. Gain practical skills in stability analysis using eigenvalues and eigenvectors.

• YouTube
• 26 minutes
• On-Demand
• Free Video

ICTP Mathematics

Stabilization of Nonlinear Systems by Oscillating Controls with Application

Explore nonlinear system stabilization using oscillating controls, with applications in nonholonomic and fluid dynamics. Covers control design, Lie brackets, and energy cascades.

• YouTube
• 1 hour
• On-Demand
• Free Video

International Centre for Theoretical Sciences

Capturing Turbulent Dynamics and Statistics in Experiments Using Exact Coherent States

Explore turbulent dynamics using Exact Coherent States, revealing coherent structures in experiments, forecasting turbulent evolution, and providing a geometric description of transient turbulence.

• YouTube
• 1 hour 10 minutes
• On-Demand
• Free Video

International Centre for Theoretical Sciences

Introduction to Dynamical Systems - Lecture 1

Explore dynamical systems, from linear ODEs to nonlinear chaos. Learn about equilibrium points, eigenvalues, attractors, and bifurcations. Gain insights into Lorenz systems, Poincaré maps, and iterative methods.

• YouTube
• 1 hour 14 minutes
• On-Demand
• Free Video

Steve Brunton

Numerical Simulation of Ordinary Differential Equations - Integrating ODEs

Explore numerical integration of ODEs to analyze nonlinear systems and generate trajectories. Learn techniques for solving complex dynamics where analytic methods fall short.

• YouTube
• 24 minutes
• On-Demand
• Free Video

Steve Brunton

Linearizing Around a Fixed Point - Control Bootcamp

Explore linearization of nonlinear systems around fixed points, demonstrated with a simple pendulum example using both manual calculations and MATLAB implementation.

• YouTube
• 31 minutes
• On-Demand
• Free Video

Fields Institute

Tame Control Theory - Lecture 5

Explore advanced concepts in tame control theory, focusing on phenomena over real fields. Delve into graduate-level mathematical analysis and applications.

• YouTube
• 1 hour 37 minutes
• On-Demand
• Free Video

Fields Institute

Tame Phenomena Over the Real Field - Graduate Course Lecture 1

Explore fundamental concepts of tame control theory, focusing on real field applications and advanced mathematical principles in this graduate-level lecture.

• YouTube
• 46 minutes
• On-Demand
• Free Video

ICTP Mathematics

Dynamical Systems - Lecture 02

Explore advanced concepts in dynamical systems theory, focusing on mathematical principles and applications in complex systems analysis and modeling.

• YouTube
• 1 hour 30 minutes
• On-Demand
• Free Video

ICTP Mathematics

Dynamical Systems - Lecture 03

Explore advanced concepts in dynamical systems theory, focusing on mathematical principles and applications in complex systems analysis and modeling.

• YouTube
• 1 hour 27 minutes
• On-Demand
• Free Video