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I have the following system of reactions: \begin{align} M & \xrightarrow{\lambda(M,W)}M+M \\ W & \xrightarrow{\lambda(M,W)}W+W \\ M & \xrightarrow{\mu} \emptyset \\ W & \xrightarrow{\mu} \emptyset \end{align} Where $\emptyset$ encodes no species and $\lambda(W,M) = \mu+c(N-(W+\delta M))$ where $\mu , c , N > 0$ and $0 < \delta < 1$. Both $\lambda(W,M)$ and $\mu$ are the rates per individual.

I come from a mathematical background and I am trying to apply the Law of Mass action to the above system. I am confused since in the right hand side the $M$ and $W$ appears twice. What are the rates of of $M$ and $W$ of the above system?

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    $\begingroup$ As it stands, the system looks quite unchemical. $\endgroup$ – Ivan Neretin Jan 6 at 18:03
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    $\begingroup$ $\ce{M -> 2M}$ makes no sense chemically. Can you explain the proposed chemistry better? $\endgroup$ – MaxW Jan 6 at 18:55
  • $\begingroup$ $\ce{M -> \varnothing}$ doesn't make any sense because it is a violation of conservation of matter. It goes to something, even if you don't care what it is. $\endgroup$ – Zhe Jan 7 at 15:29

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