Lorenz System

Strange attractor

Author

Sushovan Majhi

Published

September 12, 2022

The System

Lorenz system is a system of (non-linear) ordinary differential equations. \[\begin{aligned} \dot{x} &= \sigma(y-x)\\ \dot{y} &= x(\rho-z)-y\\ \dot{z} &= xy-\beta z \end{aligned}\]

Here \(\sigma,\rho,\text{ and }\beta\) are system parameters.

Evolution Projected on Y-Z Plane

Time-series from the Z-axis

Takens’ Embedding