The multi-patch logistic equation

<p style='text-indent:20px;'>The paper considers a <inline-formula><tex-math id="M1">\begin{document}$ n $\end{document}</tex-math></inline-formula>-patch model with migration terms, where each patch follows logistic law. First, we give some properties of the total equilibrium population. In particular cases, determine conditions under which fragmentation and can lead to population might be greater or smaller than sum id="M2">\begin{document}$ $\end{document}</tex-math></inline-formula> carrying capacities. Second, in case perfect mixing, i.e when rate tends infinity, law capacity general is different from id="M3">\begin{document}$ Finally, for three-patch show numerically that increase number patches two three gives new behavior dynamics as function rate.</p>