Help! How would I find the equilibrium points of this system?

Question

I have the discrete-time dynamical system m_t+1=0.6m_t+3 with m₀=0. What would be the equilibrium point(s) of the system?

i replaced m_t with x to then get x=7.5 as the equilibrium point. would this be correct or are there more points of equilibrium?

Answer 1

Yes, your value of m_t leads to m_t+1 = m_t which means change has stopped. 7.5 is the equilibrium for all initial m.

Answer 2

Yes, since it's a linear system, the equilibrium is unique, at m = 3/(1 – 0.6) = 7.5.