Hello all. I am a biologist and I have a discrete system I created and I want to force an internal equilibrium to be unstable given conditions on my control variable.

I just want someone to tell me if they agree with my logic. this is what I have done:

To prove stability in a discrete system you usually use the jury conditions:
|TraceJ| < 1 + detJ < 2 . Where J is the Jacobian.

If I show that |TraceJ| > 2, have I shown instability for the equilibrium point in question? I sure hope so, because I spent hours solving for my control variable.

HELP will be taken seriously. So please give your opinion.