Nonlinear Dynamics Courses and Certifications

Nonlinear Dynamics: Mathematical and Computational Approaches

Study maps and flows: unpack state space, attractors, bifurcations and the Feigenbaum number, solve chaotic systems numerically, and apply nonlinear time-series analysis to real data.

• Complexity Explorer
• Self-Paced
• Free Certificate

A Visual Approach to Nonlinear Dynamics

Build intuition for nonlinear systems through animated visuals: fixed points, bifurcations, limit cycles, chaos and strange attractors in the logistic map, Van der Pol oscillator and Lorenz system.

• Complexity Explorer
• Self-Paced
• Free Certificate

Nonlinear Dynamics and Chaos

Explore nonlinear differential equations, chaotic systems, and numerical and analytical techniques for understanding their behavior.

• Swayam
• Available until Oct 9, 2026
• Free Online Course

NPTEL;  IIT Madras

Topics in Nonlinear Dynamics

Explore nonlinear dynamical behavior through phase-space flows, Hamiltonian dynamics, bifurcations, limit cycles, and discrete-time systems.

• YouTube
• 1 day 5 hours
• Self-Paced
• Free Video

NPTEL;  IIT Madras

Topics in Nonlinear Dynamics

This is a basic course in classical mechanics at the senior undergraduate/ master's level. It covers the standard topics in this subject, including the Lagrangian and Hamiltonian formalisms. It also places the subject in the broader context of classical…

• YouTube
• 1 day 5 hours
• Self-Paced
• Free Video

Complexity Explorer

Nonlinear Dynamics - Introduction to Chaos Theory and Complex Systems

Explore chaotic systems, bifurcations, attractors, and fractal dimensions through mathematical modeling, ODE solving, and time series analysis techniques.

• YouTube
• 9 hours 43 minutes
• Self-Paced
• Free Video

Steve Brunton

Sparse Nonlinear Dynamics Models with SINDy - The Library of Candidate Nonlinearities

Learn to design SINDy libraries that encode control, rational dynamics, dimensionality limits, and physical symmetries for sparse model discovery.

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

Steve Brunton

Koopman Observable Subspaces and Finite Linear Representations of Nonlinear Dynamics for Control

Explores Koopman observable subspaces for representing nonlinear dynamics with finite-dimensional linear systems and designing nonlinear optimal controllers.

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

Complexity Explorer

A Visual Approach to Nonlinear Dynamics

Explore nonlinear dynamics through visual geometric approaches, covering 1D/2D/3D systems, bifurcations, chaos, and real-world applications like species competition and Lorenz models.

• YouTube
• 4 hours 40 minutes
• Self-Paced
• Free Video

Complexity Explorer

A Visual Approach to Nonlinear Dynamics - 3-Species Competition and Stability of Fixed Points - Unit 4.1

Explore stability analysis of fixed points in 3-species competition models through visual nonlinear dynamics techniques with Professor Sid Redner from Santa Fe Institute.

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

Nonlinear Dynamics and Chaos

An informal, geometrically intuitive introduction to nonlinear dynamics, from bifurcations and oscillators to Lorenz chaos, fractals, and strange attractors.

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

Nonlinear Dynamics: Mathematical and Computational Approaches

71 ratings

This course provides a broad introduction to the field of nonlinear dynamics, focusing both on the mathematics and the computational tools that are so important in the study of chaotic systems.

• Complexity Explorer
• 11 weeks
• No Longer Offered
• Free Certificate

Nonlinear Dynamical System and Application

Study nonlinear dynamical systems through bifurcation, center manifold, normal form, chaos, and applications to neuron and railway wheelset models.

• XuetangX
• Self-Paced
• Free Online Course

Steve Brunton

Linearizing Nonlinear Differential Equations Near a Fixed Point

Linearize nonlinear differential equations near fixed points using Taylor expansion and Jacobian matrices to analyze local stability.

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

Steve Brunton

Koopman Spectral Analysis - Overview

Introduces Koopman operator theory for representing nonlinear dynamical systems linearly through data-driven measurements, eigenfunctions, invariant subspaces, and dynamic mode decomposition.

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