Raaja
Not sure why the 2nd switching in `\ifnum` is not happening. That is in the first part, based on my input definition, the ODE grows, and second, based on the conditional, the ODE decays. However, what I want is that it needs to grow back - decay again in a cycle. Currently, this is what I have, for some reasons, my script is stuck in some sort of loop and I am not able to get it out.
Any help is appreciated.
```
%&lualatex
% !TeX TXS-program:compile = txs:///lualatex/[--shell-escape]
\documentclass[border=5mm,tikz,convert={density=1200,outext=.png}]{standalone}
\usepackage{ifthen}
\usetikzlibrary{calc}
%https://tex.stackexchange.com/questions/471741/draw-solution-curves-of-a-differential-equation-with-tikz?noredirect=1&lq=1
%https://tex.stackexchange.com/questions/294686/ifthenelse-inside-tikz-not-working
\begin{document}
\begin{tikzpicture}[declare function={f(\x,\y)=(-1*\x) + \y;}]
\def\xmax{10} \def\xmin{0}
\def\ymax{5} \def\ymin{0}
\def\xini{0} \def\uhot{5} \def\ucold{0}
\def\tmax{10} \def\tmin{0}
% \def\nx{15} % \def\ny{15}
% \pgfmathsetmacro{\hx}{(\xmax-\xmin)/\nx}
% \pgfmathsetmacro{\hy}{(\ymax-\ymin)/\ny}
% \foreach \i in {0,...,\nx}
% \foreach \j in {0,...,\ny}{
% \draw[teal,-stealth]
% ({\xmin+\i*\hx},{\ymin+\j*\hy}) -- ++ ({atan2(f({\xmin+\i*\hx},{\ymin+\j*\hy}),1)}:0.1);
% }
\pgfmathsetmacro{\stept}{0.01}
\pgfmathsetmacro{\nextt}{\tmin+\stept}
\pgfmathsetmacro{\nextnextt}{\tmin+2*\stept}
\pgfmathsetmacro{\tfin}{\tmax+0.1}
\pgfmathsetmacro{\tref}{\tmin}
\pgfmathsetmacro{\u}{\uhot}
\pgfmathsetmacro{\tcold}{0.2}
\pgfmathsetmacro{\ccount}{1}
\xdef\lstX{(\tmin,\xini)}
\pgfmathsetmacro{\myy}{\xini}
\pgfmathsetmacro{\rflag}{1}
\foreach \x in {\nextt,\nextnextt,...,\tfin}
{\pgfmathparse{(\x - (0.4*\ccount)) < 0.00001 ? int(1) : int(0)}
\pgfmathsetmacro{\rtest}{\pgfmathresult}
\pgfmathparse{and(\rtest, \rflag)}
\pgfmathsetmacro{\rrtest}{\pgfmathresult}
\ifnum\rrtest=0
\pgfmathsetmacro{\u}{\ucold}
\pgfmathsetmacro{\tref}{\x}
\pgfmathsetmacro{\rflag}{0}
\else
\pgfmathparse{(\x - \tref - \tcold) < 0.00001 ? int(1) : int(0)}
\pgfmathsetmacro{\crtest}{\pgfmathresult}
\ifnum\crtest=0
\pgfmathsetmacro{\u}{\uhot}
\pgfmathsetmacro{\ccount}{\ccount+1}
\pgfmathsetmacro{\rflag}{1}
\fi
\fi
{
\pgfmathsetmacro{\myy}{\myy+f(\myy,\u)*\stept}
\xdef\myy{\myy}
\xdef\lstX{\lstX (\x,\myy)}
}
}
\draw[red,ultra thick] plot[smooth] coordinates {\lstX};
% grid
\draw (\xmin,\ymin) rectangle ($(\xmax,\ymax)+(1mm,1mm)$);
% \draw (current bounding box.north) node[above=5mm]{$y'=x^2+y^2-1$.};
% ticks
\foreach \i in {0,1,...,\xmax}
\draw (\i,\ymin) node[below]{$\i$}--++(90:.5mm);
\foreach \i in {0,\ymax}
\draw (\xmin,\i) node[left]{$\i$}--++(0:.5mm);
\end{tikzpicture}
\end{document}
```
What would be more nice is that, a `mesh` like coloring for the figure.
Ideally what I am trying to do is something like this:
