Nonlinear Dynamics and Chaos

First published: 2012

Brief summary

MIT OCW course on oscillations, bifurcations and chaos.

Article

Nonlinear dynamics studies systems whose responses are not directly proportional to their inputs or current states. Even models with only a few variables can display fixed points, periodic oscillations, multiple stable states and irregular behaviour.

The MIT course introduces differential-equation models of dissipative systems and examines oscillators, phase-plane methods, stability and bifurcations. A bifurcation occurs when a gradual change in a parameter produces a qualitative change in the system’s long-term behaviour.

Chaos is deterministic behaviour that is highly sensitive to initial conditions. Nearby trajectories can separate rapidly while remaining confined to a structured region of state space, producing irregular motion without requiring random forcing.

Numerical experiments are important because nonlinear equations often lack closed-form solutions. Simulations, return maps and graphical methods are used to identify transitions, attractors and parameter ranges associated with periodic or chaotic behaviour.

Source details and credits

• Source / publisher: MIT OCW
• Source type: Course material
• URL type: WWW
• Credits: MIT OCW
• URL: https://ocw.mit.edu/courses/18-353j-nonlinear-dynamics-i-chaos-fall-2012/