Chaos Theory Courses and Certifications

Fields Institute

Reservoir Computing - Machine Learning and Dynamical Systems

Explore cutting-edge reservoir computing techniques across hardware implementations, chaos prediction, and applications in turbulence, finance, and photonics through expert presentations.

• YouTube
• 8 hours 24 minutes
• Self-Paced
• Free Video

ICTP Mathematics

Dynamical Systems

Explore mathematical systems that evolve over time through 20 comprehensive lectures covering fundamental theory, applications, and advanced concepts in dynamical systems.

• YouTube
• 1 day 4 hours 18 minutes
• Self-Paced
• Free Video

Centre de recherches mathématiques - CRM

CRM CAMP in Nonlinear Analysis - Computer-Assisted Methods of Proof

Explore computer-assisted proof methods for dynamical systems and nonlinear analysis through expert presentations on chaos, bifurcations, and rigorous numerical techniques.

• YouTube
• 2 days 10 hours 41 minutes
• Self-Paced
• Free Video

Ross Dynamics Lab

Bifurcation Theory - Saddle-Node, Hopf, Transcritical, Pitchfork

2 ratings

Explore saddle-node, transcritical, pitchfork, and Hopf bifurcations in dynamical systems. Learn how these phenomena affect phase portraits and system behavior as parameters change.

• YouTube
• 1 hour 17 minutes
• Self-Paced
• Free Video

Harnessing Chaos and Predicting the Unpredictable with Artificial Intelligence

Explore how Reservoir Computing and AI can predict chaotic systems like weather and brain dynamics, pushing beyond traditional forecasting limits and combining knowledge-free and knowledge-based approaches.

• YouTube
• 1 hour 20 minutes
• Self-Paced
• Free Video

Topology Shapes Dynamics of Higher-order Networks

Exploring how higher-order network interactions influence non-linear dynamics, synchronization, and percolation in complex systems like brain networks and climate patterns.

• YouTube
• 56 minutes
• Self-Paced
• Free Video

Making Sense of Chaos - A Better Economics for a Better World

Explore how complexity economics can revolutionize our understanding of global economic challenges and lead to better predictions and solutions for a more sustainable future.

• YouTube
• 1 hour 38 minutes
• Self-Paced
• Free Video

NPTEL;  IIT Delhi

Introductory Non-Linear Dynamics

This course is designed to introduce students to the basic ideas of Dynamical systems, Stability, and chaos, largely using Iterative mappings as the model. The course will focus on qualitative ideas and will require students to explore dynamics through s…

• YouTube
• 6 hours
• Self-Paced
• Free Video

Ross Dynamics Lab

Generating Function of a Canonical Transformation - Examples and the Big Picture

Explore generating functions for canonical transformations in Hamiltonian systems. Learn about harmonic oscillator examples, near-identity transformations, and connections to quantum mechanics and gauge invariance.

• YouTube
• 57 minutes
• Self-Paced
• Free Video

Ross Dynamics Lab

Stability of Periodic Orbits - Floquet Theory - Stable and Unstable Invariant Manifolds

Explore stability of periodic orbits using Floquet theory. Learn about monodromy matrices, Floquet multipliers, and invariant manifolds in Hamiltonian systems. Understand the foundations of chaos in dynamical systems.

• YouTube
• 1 hour 13 minutes
• Self-Paced
• Free Video

International Centre for Theoretical Sciences

Quantum Aspects of Black Holes - Lecture 2

Explores quantum aspects of black holes, covering Schwarzschild solutions, ER=EPR, AMPS paradox, 2D gravity models, chaos in quantum systems, and the connection between black holes and quantum information theory.

• YouTube
• 1 hour 37 minutes
• Self-Paced
• Free Video

International Centre for Theoretical Sciences

Chimera States in Mechanical Oscillator Networks by Shashi Thutupalli

Explore chimera states in mechanical oscillator networks, covering synchronization, Kuramoto model, coupled populations, experimental designs, and various chimera phenomena in complex systems.

• YouTube
• 45 minutes
• Self-Paced
• 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
• Self-Paced
• Free Video

Steve Brunton

Numerical Integration of Chaotic Dynamics - Uncertainty Propagation & Vectorized Integration

Explore chaos and uncertainty propagation in dynamical systems through numerical integration. Learn efficient vectorization techniques in Python and MATLAB for faster computations.

• YouTube
• 20 minutes
• Self-Paced
• Free Video

Steve Brunton

Hankel Alternative View of Koopman - HAVOK Analysis

Decompose chaos into linear systems with intermittent forcing using HAVOK analysis. Learn to build linear regression models on eigen-time-delay coordinates for complex dynamical systems.

• YouTube
• 23 minutes
• Self-Paced
• Free Video