This is my working example:
\documentclass{article}
\usepackage[utf8]{inputenc}
\begin{document}
\section{table of model and predictions}
\begin{table}[h]
\begin{tabular}{lllll}
%\begin{longtable}{lllll}
\hline
& & & & \
\multicolumn{5}{c}{expandedsystem} \
\multicolumn{1}{c}{} & & & & \ \hline
& & & & \
\textbf{Dynamical Systems} & & Original Systems & & System Expanded \
\textbf{} & & & & \ \hline
& & & & \
Saddle-Node & & & & $\dot{\alpha} = 0.8 + 4e-10t + 3e-3t^2$ \
& & $\dot{x} = \alpha- x^3$ & & $\dot{x} = \alpha- x^3$ \
& & & & \
\hline
& & & & \
Pitchfork & & & & $\dot{\alpha} =4.5+2.16t + 3.39t^2$ \
& & $\dot{x} = \alpha- x^2$ & & $\dot{x} = \alpha- x^2$ \
& & & & \
\hline
& & & & \
Hopf & & & & $\dot{\alpha} =-t+t^2-t^3$ \
& & & & \
& & $\dot{x}{1} =\alpha x{1}-x_{2}-x_{1}\left(x_{1}^{2}+x_{2}^{2}\right)$ & & $\dot{x}{1} =\alpha x{1}-x_{2}-x_{1}\left(x_{1}^{2}+x_{2}^{2}\right)$ \
& & & & \
& & $\dot{x}{2} =x{1}+\alpha x_{2}-x_{2}\left(x_{1}^{2}+x_{2}^{2}\right)$ & & $\dot{x}{2} =x{1}+\alpha x_{2}-x_{2}\left(x_{1}^{2}+x_{2}^{2}\right)$ \
& & & & \
\hline
& & & & \
Lorentz & & & & $\dot{\rho} =1.1 + 0.92t -0.027 t^2+ 3^{-4}t^3$ \
& & & & \
& & $\dot{x}= \sigma(y-x)$ & & $\dot{x}= \sigma(y-x)$ \
& & & & \
& & $\dot{y}= x(\rho-z)-y$ & & $\dot{y}= x(\rho-z)-y$ \
& & & & \
& & $\dot{z}= x y-\beta z$ & & $\dot{z}= x y-\beta z$ \
& & & & \
\hline
& & & & \
Van Der Pol & & & & $\dot{\alpha} =1.1 + 0.92t -0.027 t^2+ 3^{-4}t^3$ \
& & & & \
& & $\dot{x}= y$ & & $\dot{x}= y$ \
& & & & \
& & $\dot{y}= \alpha\left(1-x^{2}\right) y-x$ & & $\dot{y}= \alpha\left(1-x^{2}\right) y-x$ \
& & & & \
\hline
& & & & \
Hodgin-Huxley & & & & $ \dot{\alpha} = 1.1 + 0.92t -0.027 t^2+ 3^{-4}t^3$ \
& & & & \
& & $\dot{n}= \alpha_{n}\left(V_{m}\right)(1-n)-\beta_{n}\left(V_{m}\right) n$ & & $\dot{n}= \alpha_{n}\left(V_{m}\right)(1-n)-\beta_{n}\left(V_{m}\right) n$ \
& & & & \
& & $\dot{m}= \alpha_{m}\left(V_{m}\right)(1-m)-\beta_{m}\left(V_{m}\right) m$ & & $\dot{m}= \alpha_{m}\left(V_{m}\right)(1-m)-\beta_{m}\left(V_{m}\right) m$ \
& & & & \
& & $\dot{h}= \alpha_{h}\left(V_{m}\right)(1-h)-\beta_{h}\left(V_{m}\right) h$ & & $\dot{h}= \alpha_{h}\left(V_{m}\right)(1-h)-\beta_{h}\left(V_{m}\right) h$ \
& & & & \
\hline
& & & & \
Fitzhugh- Nagumo & & & & $\dot{\alpha} = 1.1 + 0.92t$ \
& & $\dot{u}= \epsilon g(u) -w + I$ & & $\dot{u}= \epsilon g(u) -w + I$ \
& & & & \
& & $\dot{w}= u - aw$ & & $\dot{w}= u - aw$ \
& & & & \
\hline
& & & & \
Bistable Toggle Switch & & & & $\dot{\alpha} = 1.1 + 0.92t -0.027 t^2+ 3^{-4}t^3$ \
& & $\dot{x}_1 = \frac{a_1}{1+(x_2)^{n_1}}-d_1x_1$ & & $\dot{x}_1 = \frac{a_1}{1+(x_2)^{n_1}}-d_1x_1$ \
& & & & \
& & $\dot{x_2} = \frac{a_2}{1+(x_1)^{n_2}}-d_2x_2$ & & $\dot{x_2} = \frac{a_2}{1+(x_1)^{n_2}}-d_2x_2$ \
& & & & \
& & & & \ \hline
\end{tabular}
\end{table}
%\end{longtable}
%\end{table}
\end{document}
when I use longtable the table shows unexpectedly extrange: This is the code:
\documentclass{article}
\usepackage[utf8]{inputenc}
\begin{document}
\section{table of model and predictions}
\begin{longtable}{lllll}
\hline
& & & & \
\multicolumn{5}{c}{expandedsystem} \
\multicolumn{1}{c}{} & & & & \ \hline
& & & & \
\textbf{Dynamical Systems} & & Original Systems & & System Expanded \
\textbf{} & & & & \ \hline
& & & & \
Saddle-Node & & & & $\dot{\alpha} = 0.8 + 4e-10t + 3e-3t^2$ \
& & $\dot{x} = \alpha- x^3$ & & $\dot{x} = \alpha- x^3$ \
& & & & \
\hline
& & & & \
Pitchfork & & & & $\dot{\alpha} =4.5+2.16t + 3.39t^2$ \
& & $\dot{x} = \alpha- x^2$ & & $\dot{x} = \alpha- x^2$ \
& & & & \
\hline
& & & & \
Hopf & & & & $\dot{\alpha} =-t+t^2-t^3$ \
& & & & \
& & $\dot{x}{1} =\alpha x{1}-x_{2}-x_{1}\left(x_{1}^{2}+x_{2}^{2}\right)$ & & $\dot{x}{1} =\alpha x{1}-x_{2}-x_{1}\left(x_{1}^{2}+x_{2}^{2}\right)$ \
& & & & \
& & $\dot{x}{2} =x{1}+\alpha x_{2}-x_{2}\left(x_{1}^{2}+x_{2}^{2}\right)$ & & $\dot{x}{2} =x{1}+\alpha x_{2}-x_{2}\left(x_{1}^{2}+x_{2}^{2}\right)$ \
& & & & \
\hline
& & & & \
Lorentz & & & & $\dot{\rho} =1.1 + 0.92t -0.027 t^2+ 3^{-4}t^3$ \
& & & & \
& & $\dot{x}= \sigma(y-x)$ & & $\dot{x}= \sigma(y-x)$ \
& & & & \
& & $\dot{y}= x(\rho-z)-y$ & & $\dot{y}= x(\rho-z)-y$ \
& & & & \
& & $\dot{z}= x y-\beta z$ & & $\dot{z}= x y-\beta z$ \
& & & & \
\hline
& & & & \
Van Der Pol & & & & $\dot{\alpha} =1.1 + 0.92t -0.027 t^2+ 3^{-4}t^3$ \
& & & & \
& & $\dot{x}= y$ & & $\dot{x}= y$ \
& & & & \
& & $\dot{y}= \alpha\left(1-x^{2}\right) y-x$ & & $\dot{y}= \alpha\left(1-x^{2}\right) y-x$ \
& & & & \
\hline
& & & & \
Hodgin-Huxley & & & & $ \dot{\alpha} = 1.1 + 0.92t -0.027 t^2+ 3^{-4}t^3$ \
& & & & \
& & $\dot{n}= \alpha_{n}\left(V_{m}\right)(1-n)-\beta_{n}\left(V_{m}\right) n$ & & $\dot{n}= \alpha_{n}\left(V_{m}\right)(1-n)-\beta_{n}\left(V_{m}\right) n$ \
& & & & \
& & $\dot{m}= \alpha_{m}\left(V_{m}\right)(1-m)-\beta_{m}\left(V_{m}\right) m$ & & $\dot{m}= \alpha_{m}\left(V_{m}\right)(1-m)-\beta_{m}\left(V_{m}\right) m$ \
& & & & \
& & $\dot{h}= \alpha_{h}\left(V_{m}\right)(1-h)-\beta_{h}\left(V_{m}\right) h$ & & $\dot{h}= \alpha_{h}\left(V_{m}\right)(1-h)-\beta_{h}\left(V_{m}\right) h$ \
& & & & \
\hline
& & & & \
Fitzhugh- Nagumo & & & & $\dot{\alpha} = 1.1 + 0.92t$ \
& & $\dot{u}= \epsilon g(u) -w + I$ & & $\dot{u}= \epsilon g(u) -w + I$ \
& & & & \
& & $\dot{w}= u - aw$ & & $\dot{w}= u - aw$ \
& & & & \
\hline
& & & & \
Bistable Toggle Switch & & & & $\dot{\alpha} = 1.1 + 0.92t -0.027 t^2+ 3^{-4}t^3$ \
& & $\dot{x}_1 = \frac{a_1}{1+(x_2)^{n_1}}-d_1x_1$ & & $\dot{x}_1 = \frac{a_1}{1+(x_2)^{n_1}}-d_1x_1$ \
& & & & \
& & $\dot{x_2} = \frac{a_2}{1+(x_1)^{n_2}}-d_2x_2$ & & $\dot{x_2} = \frac{a_2}{1+(x_1)^{n_2}}-d_2x_2$ \
& & & & \
& & & & \ \hline
\end{longtable}
\end{document}




\usepackage{longtable}. When I add that, the output for me does not look like your second image, but more like your first image split over two pages as I think you wanted. – frabjous Apr 09 '22 at 15:33\usepackage{longtable}, I do get your image. But just above that, I get thelllll. I also get 133 errors, the first one being "Environment longtable undefined". Don't ignore errors. My wild guess is that you have columns 2 and 4 empty to spread out the columns a bit. Don't do that; use https://tex.stackexchange.com/q/16519/107497 instead. – Teepeemm Apr 09 '22 at 15:49