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.

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Kinetics Modeling

**Physics Forums | Science Articles, Homework Help, Discussion**