Update cheatsheet.fr.md

12.temporary_ins/32.sets-systems/30.n3/20.systems/20.overview/cheatsheet.fr.md

@@ -429,31 +429,22 @@ L'une représente des proies et l'autre des prédateurs.
      <br>
    * L'état **$`\mathbf{(X_1=D_2/C_2\,,\,X_2=C_1/D_1)}`$** est l'*unique cas stationnaire* intéressant.   
      <br>
-     **$`\left.\begin{array}{l}
+     **$`\mathbf{\left.\begin{array}{l}
       \forall t \in \mathbb{R},\\
       X_1(t) = \dfrac{D_2}{C_2} =X_1\\
       X_2(t) = \dfrac{C_1}{D_1} = X_2
-      \end{array}\right\}`$**
+      \end{array}\right\}}`$**
       $`\Longrightarrow\left\{\begin{array}{l}
       \forall t \in \mathbb{R}, \\
-      \left.\Dfrac{dX_1}{dt}\right\vert_t=+C_1\,X_1(t)-D_1\,X_1(t)X_2(t)\\
-      \left.\Dfrac{dX_1}{dt}\right\vert_t=-D_2\,X_2(t)+C_2\,X_1(t)X_2(t)
+      \left.\dfrac{dX_1}{dt}\right\vert_t=+C_1\,\dfrac{D_2}{C_2}-D_1\,\dfrac{D_2}{C_2}\dfrac{C_1}{D_1}\\
+      \left.\dfrac{dX_1}{dt}\right\vert_t=-D_2\,\dfrac{C_1}{D_1}+C_2\,\dfrac{D_2}{C_2}\dfrac{C_1}{D_1}
       \end{array}\right.`$
-      $`\Longrightarrow\left\{\begin{array}{l}
-      \forall t \in \mathbb{R}, \\
-      \left.\Dfrac{dX_1}{dt}\right\vert_t=+C_1\,\dfrac{D_2}{C_2}-D_1\,\dfrac{D_2}{C_2}\dfrac{C_1}{D_1}\\
-      \left.\Dfrac{dX_1}{dt}\right\vert_t=-D_2\,\dfrac{C_1}{D_1}+C_2\,\dfrac{D_2}{C_2}\dfrac{C_1}{D_1}
-      \end{array}\right.`$
-      $`\Longrightarrow\left\{\begin{array}{l}
+      **$`\mathbf{\Longrightarrow\left\{\begin{array}{l}
       \forall t \in \mathbb{R}, \\
-      \left.\Dfrac{dX_1}{dt}\right\vert_t=+C_1\,\dfrac{D_2}{C_2}-D_1\,\dfrac{D_2}{C_2}\dfrac{C_1}{D_1}\\
-      \left.\Dfrac{dX_1}{dt}\right\vert_t=-D_2\,\dfrac{C_1}{D_1}+C_2\,\dfrac{D_2}{C_2}\dfrac{C_1}{D_1}
-      \end{array}\right.`$
-      
-
-C_1(t)=\dfrac{D_2}{C_2}=C_1\\
-      C_2(t)=\dfrac{C_1}{D_1}=C_2
-      \end{array}\right\}`$
+      \left.\dfrac{dX_1}{dt}\right\vert_t=0\\
+      \left.\dfrac{dX_1}{dt}\right\vert_t=0
+      \end{array}\right.}`$**
+      *$`\mathbf{\Longrightarrow} (X_1,X_2)`$* est *stationnaire*.
       
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