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Could anyone can help me how to type the following equations in latex?

equation

Thank you very much

6

enter image description here

\documentclass{article}

\usepackage{amsmath,bm,eqparbox}
\newcommand{\tsum}{\textstyle\sum}

\begin{document}

\begin{subequations}
\begin{align}
  \left\{
    \begin{aligned}
      \epsilon\, \dot{z}^i  &= \eqmakebox[RHS][l]{$-(z^i + u^i) - \sum_{i = j}^N \bm{L}_{ij} (z^j + \nu^j)$,} \\
      \eqmakebox[LHS][r]{$\epsilon\, \dot{\nu}^i$} &= \tsum_{j = 1}^N \bm{L}_{ji} z^j,
    \end{aligned}
  \right.\kern-\nulldelimiterspace \\
  \left\{
    \begin{aligned}
      \epsilon\, \dot{y}^i  &= \eqmakebox[RHS][l]{$-(y^i + \dot{u}^i) - \sum_{i = j}^N \bm{L}_{ij} (y^j + \mu^j)$,} \\
      \eqmakebox[LHS][r]{$\epsilon\, \dot{\mu}^i$} &= \tsum_{j = 1}^N \bm{L}_{ji} y^j,
    \end{aligned}
  \right.\kern-\nulldelimiterspace \\
  \eqmakebox[LHS][r]{$\dot{x}^i$} = \eqmakebox[RHS][l]{$-\beta^i x^i - \beta^i z^i - y^i$.}
\end{align}
\end{subequations}

\end{document}

eqparbox ensures that we can place content in boxes that will be the same width. This helps with alignment across the structures (aligned) within align. Minor removal of \kerning as a result of a blank \right. delimiter aligns the equations as needed.

One could also have used a cases environment to achieve the braces sub-equations.

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