Consider the toggle switch model
Here, we are going to explore the parameter space that makes the system work as a toggle switch. To do so, answer the following questions:
(i) Consider m = n = 1. Determine the number and stability of the equilibria as the values of βA and βB are changed.
(ii) Consider m = 1 and n > 1 and determine the number and stability of the equilibria (as other parameters change).
(iii) Consider m = n = 2. Determine parameter conditions on βA, βB, γ, K for which the system is bistable, i.e., there are two stable steady states.