Dynamical Systems & Chaos Courses and Certifications

Neuronal Dynamics

The activity of neurons in the brain and the code used by these neurons is described by mathematical neuron models at different levels of detail.

• edX
• 7 weeks, 5-7 hours a week
• Self-Paced
• Free Online Course (Audit)

Mastering Differential Equations: The Visual Method

52 ratings at The Great Courses Plus

Embark on an amazing mathematical journey in 24 intellectually stimulating and visually engaging half hour lectures.

• The Great Courses Plus
• 12 hours 33 minutes
• Self-Paced
• Free Trial Available

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 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

IIT Roorkee;  NPTEL

Environmental Modeling and Simulation

Builds environmental models and simulations using nonlinear dynamics, Monte Carlo methods, and MATLAB or Octave across ecological and pollution systems.

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

IIT Kanpur;  NPTEL

Ordinary Differential Equations

Qualitative and geometric analysis of ordinary differential equations, from existence and linear systems to phase portraits, periodic behavior, limit cycles, and stability.

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

IIT Kharagpur;  NPTEL

Advanced Theory of Ordinary Differential Equations

Explores advanced ODE theory from existence and stability through chaos, singular perturbations, bifurcations, oscillations, boundary-value problems, and Laplace-transform solutions.

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

IIT Madras;  NPTEL

Nonlinear Dynamical Systems and Control

Analyzes nonlinear-system stability with Lyapunov methods and applies them to robust, adaptive, optimal, and model predictive control.

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

Introduction to Multi-Agent Systems

Study networked dynamical systems, graph theory, controllability, and consensus protocols for coordinated robots, autonomous vehicles, oscillator networks, and social networks.

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

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

Steve Brunton

Linearizing Around a Fixed Point - Control Bootcamp

Learn to linearize a nonlinear system around a fixed point using a simple pendulum example by hand and in MATLAB.

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

The Royal Institution

Chaos Theory and Geometry - Can They Predict Our World? With Tim Palmer

Explains how fractal geometry frames the predictability of chaotic systems, from hurricane forecasts to questions in quantum physics.

• YouTube
• 1 hour 10 minutes
• Self-Paced
• Free Video

Professor Leonard

Equilibrium Solutions and Stability of Differential Equations

Explores equilibrium solutions and how critical points determine increasing and decreasing population behavior in differential equations.

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