The larger the characteristic variance, the closer (g^) will be to unity.
So, if target firing rates are chosen to make the characteristic variance (nu^) sufficiently large, then an integrator achieved in this way is robust to variation in characteristic variance (nu^) (and unaffected by variation in (mu^)).
However, if many neurons have high characteristic variance, then no individual neuron will dominate the feedback signal.
Suppose that target firing rates are set such that each neuron n has characteristic variance (nu_{[n]}^).
If this large variance is the characteristic variance of the control system, then there is a fixed point of the dual control system at this value of g.
Under Theorem 1, a fixed point only exists if control system parameters are chosen to establish a characteristic variance of (nu^ > frac{eta^{2}}{2tau_{r}}).
(D) Note that, due to intrinsic noise, the firing rate variance everywhere in parameter space is larger than the characteristic variance reached at equilibrium in B. Thus, the characteristic variance of this system at equilibrium is unreachable, and dual homeostasis does not converge.
The corollary to Theorem 1 tells us that, to first approximation, the characteristic variance is proportionate to the difference between the target rates, and a large characteristic variance is achieved by setting the homeostatic target rates far apart from each other.
From this result we find that the difference between the two target firing rates plays a key role in establishing the characteristic variance at a control system fixed point.
