48  Attracting Torus System

48.1 System description

The governing equations of this chaotic system are

\[ \begin{eqnarray} \dot{x} &=& y\\ \dot{y} &=& -x-zy\\ \dot{z} &=& y^2+a+bz \end{eqnarray} \]

with \(a=-4,b=0.1\) and initial condition \((0,2,1)\).

An animation of the pre-computed solution trajectory for the given chaotic system is presented below. The trajectory, spanning 10³ seconds, is colored according to the calculated local Lyapunov exponents at each point in time.

48.2 Real-time simulation

The real-time simulation can be executed up to the designated end evolution can be explored by click-drag & scroll options in the mouse/touchpad. time as indicated below. As the simulation progresses, the 3D view of trajectory The visualization was made using P5.js.