Discrete-time dynamical system problem?
Consider the discrete-time dynamical system Nt+1 =rNt/Nt−3
, where r is a parameter.
Find all values (if they exist) of parameter r, for which the system has
(i) no equilibria,
(ii) one equilibrium
(iii) nonnegative equilibria.
Comments
A discrete-time dynamical system will have an equilibrium point when N_(t+1) = N_t for all t.
Or in other words E = N_0 = N_1 = N_2... etc, where E is the equilibrium point.