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

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 Online Course

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 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 Online Course

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 Online Course

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 Online Course

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 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 Online Course

Institute for Advanced Study

Observable Events and Typical Trajectories in Dynamical Systems - Lai-Sang Young

Explore observable events and typical trajectories in dynamical systems with Lai-Sang Young, covering SRB measures, attractors, and infinite dimensional center manifolds.

• YouTube
• 56 minutes
• On-Demand
• Free Online Course

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 Online Course

Fields Institute

Learning Dynamical Systems via Koopman Operator Regression in Reproducing Kernel Hilbert Spaces

Explore Koopman operator regression in reproducing kernel Hilbert spaces for dynamical systems, enhancing understanding of machine learning applications in complex systems analysis.

• YouTube
• 52 minutes
• On-Demand
• Free Online Course

Fields Institute

Toward a Unification of Infinities

Explore the concept of unifying different types of infinities in mathematics, delving into advanced theoretical frameworks and their implications for transseries and dynamical systems.

• YouTube
• 1 hour 8 minutes
• On-Demand
• Free Online Course

Fields Institute

Rigidity of Saddle Loops

Explore the mathematical concept of rigidity in saddle loops, focusing on their properties and applications in dynamical systems theory.

• YouTube
• 55 minutes
• On-Demand
• Free Online Course

Fields Institute

Holomorphic Continuation of R_an,exp - Germs: The Missing Lecture

Explore holomorphic continuation of R_an,exp-germs in this advanced mathematics lecture, delving into complex analysis and dynamical systems.

• YouTube
• 57 minutes
• On-Demand
• Free Online Course