Before we start, we import some preliminary libraries. We will also import (below) the accompanying `lorenz.py` file, which contains the actual solver and plotting routine.
1
Before we start, we import some preliminary libraries. We will also import (below) the accompanying
lorenz.py
file, which contains the actual solver and plotting routine.
We explore the Lorenz system of differential equations:
$$
\begin{aligned}
\dot{x} & = \sigma(y-x) \\
\dot{y} & = \rho x - y - xz \\
\dot{z} & = -\beta z + xy
\end{aligned}
$$
Let's change (\\(\sigma\\), \\(\beta\\), \\(\rho\\)) with ipywidgets and examine the trajectories.
11
We explore the Lorenz system of differential equations:
$$
\begin{aligned}
\dot{x} & = \sigma(y-x) \\
\dot{y} & = \rho x - y - xz \\
\dot{z} & = -\beta z + xy
\end{aligned}
$$
Let's change ($\sigma$, $\beta$, $\rho$) with ipywidgets and examine the trajectories.
After interacting with the system, we can take the result and perform further computations. In this case, we compute the average positions in \\(x\\), \\(y\\) and \\(z\\).
1
After interacting with the system, we can take the result and perform further computations. In this case, we compute the average positions in $x$, $y$ and $z$.