plot_timeseries (function)

Purpose

Visualizes the spatiotemporal evolution of the system state and its desymmetrized version using Hovmöller diagrams.

Parameters

• sol: A OdeSolution solution object (such as returned by solve_ivp or solve_ivp_symp) containing the system's time evolution data.

Description

This function generates two Hovmöller diagrams:

1. The raw time series of the system variable $X_n(t)$
2. A desymmetrized version using desymmetrize

Both diagrams:

• Show spatial index $n$ on the x-axis and time $t$ on the y-axis.
• Use a diverging colormap ('RdBu_r') to highlight positive and negative values.

Notes

• The desymmetrization is useful to uncover underlying coherent structures by removing global symmetries.

Output

Displays the two time series diagrams side by side with corresponding colorbars.