In a paper, I encountered a system modeled by six coupled first-order differential equations like so:(adsbygoogle = window.adsbygoogle || []).push({});

[tex]\frac{dm_i}{dt}=-m_i+\frac{\alpha}{1+p^n_j}+\alpha_0[/tex]

[tex]\frac{dp_i}{dt}=-\beta(p_i-m_i)[/tex] , where i=1,2,3 and j=3,1,2.

According to the paper, the system has a unique steady state which becomes unstable when [tex]\frac{(\beta+1)^2}{\beta}<\frac{3X^2}{4+2X}[/tex], where X is defined [tex]X=-\frac{\alpha n p^(n-1)}{(1+p^n)^2}[/tex]and p is the solution to [tex]p=\frac{\alpha}{1+p^n}+\alpha_0[/tex].

Lacking a textbook, I have had very little success in seeing how the steady state was derived. I intend to model a similar system. Can someone point me in the right way to understand these equations or show the derivation outright?

Thank you in advance.

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# Kinetics Modeling

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