How to solve Elowitz's equation for a bio model?

Question

Elowitz build a synthetic oscillatory network,but I can't solve the equation.

$\dfrac {dm_i}{dt}$=$-m_i$+$\dfrac {\alpha}{1+p_j^n}$+${\alpha}_0$

$\dfrac{dp_i}{dt}$=$-\beta(p_i-m_i)$

$i=1,2,3$

$j=2,3,1$

${m_1}(0)=10$

${m_i}(0)={p_i}(0)=0$