Dynamical Systems Courses and Certifications

Introduction to Dynamical Systems and Chaos

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In this course you'll gain an introduction to the modern study of dynamical systems, the interdisciplinary field of applied mathematics that studies systems that change over time.

• Complexity Explorer
• 10 weeks, 3-6 hours a week
• On-Demand
• Free Online Course

• Best of All Time

Introduction to Dynamical Systems and Chaos

Explore dynamical systems, chaos theory, and complex systems. Learn about bifurcations, butterfly effect, strange attractors, and pattern formation. Gain insights into predictability and complexity in nature.

• Complexity Explorer
• On-Demand
• Free Online Course

The Dynamics of Computation and the Computational Power of Dynamics

Explore the intersection of computation and dynamics, examining computational models, physical systems, and mathematical concepts to understand the nature of computation and its manifestation in various forms.

• YouTube
• 1 hour 29 minutes
• On-Demand
• Free Video

A Framework for Machine Learning of Model Error in Dynamical Systems

Explore a framework for machine learning to model error in dynamical systems, focusing on linear oscillators, partial information, and hybrid modeling techniques.

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

Demonology - Intelligence in Physics & Biology

Explore the historical role of intelligence in physics and biology, from Laplace's demon to modern information theory, and its implications for understanding natural phenomena.

• YouTube
• 1 hour 12 minutes
• On-Demand
• Free Video

Using Curvature to Understand the Structure of Dynamics

Explore curvature's role in understanding attractor dynamics and its application in time-series data reconstruction, focusing on optimal time-delay parameter selection for delay-coordinate embeddings.

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

The Statue in the Stone: How Dynamical Systems Discover Environmental Patterns

Explores how complex systems adapt to environmental patterns, favoring stable configurations that match external forces. Illustrates with toy models and swarm-robotics experiment.

• YouTube
• 59 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

MITCBMM

Dynamical Systems in Neuroscience

Explore cluster computing and OpenMind for brain and cognitive sciences, covering dynamical systems, models, and observation techniques in neuroscience research.

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

Institute for Advanced Study

On the Spatial Restricted Three-Body Problem - Agustin Moreno

Explore the spatial restricted three-body problem, global hypersurfaces, and Hamiltonian return maps. Learn about a higher-dimensional Poincaré-Birkhoff theorem and its applications to orbital dynamics.

• YouTube
• 1 hour 17 minutes
• On-Demand
• Free Video

Steve Brunton

Topics in Dynamical Systems - Fixed Points, Linearization, Invariant Manifolds, Bifurcations & Chaos

Explore dynamical systems: fixed points, linearization, manifolds, bifurcations, and chaos. Gain insights into nonlinear dynamics and their applications in describing our changing world.

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

Steve Brunton

Koopman Spectral Analysis - Overview

Explore Koopman operator theory for dynamical systems, its recent resurgence, and applications like Dynamic Mode Decomposition in this comprehensive overview.

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

Steve Brunton

Hankel Alternative View of Koopman Analysis

Decomposing chaos into linear systems with intermittent forcing using HAVOK analysis. Explores eigen-time-delay coordinates for regression models, offering new insights into complex dynamical systems.

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

ICTP Mathematics

SRB Measures and Young Towers - Lecture 4

Explore advanced techniques in dynamical systems, focusing on SRB measures and Young Towers. Learn about recent developments and applications in nonuniformly hyperbolic systems.

• YouTube
• 2 hours 23 minutes
• On-Demand
• Free Video

ICTP Mathematics

Symbolic Dynamics for Nonuniformly Hyperbolic Systems - Lecture 5

Explore advanced techniques in symbolic dynamics for complex hyperbolic systems. Gain insights into infinite Markov partitions and their applications in studying statistical properties of dynamical systems.

• YouTube
• 1 hour 29 minutes
• On-Demand
• Free Video