Help for Steady State six Coupled first order differential equations

[Goldensteev]

Hi, i am currently on a Bio/math project, one of the goals of the project is to explain the model, but unfortunately i am stuck and i can not figure out for the life of me how to prove there is a steady state :/!

http://courses.cs.washington.edu/courses/cse586/10au/repressilator.pdf


Here is the link to the Article!

The equations are in box 1 on page 3!

any tips/links to sites are of great help!

Thanks