Fig. 5

Dual homeostasis tolerates some intrinsic firing rate noise but fails to converge if noise is sufficiently strong. The dynamics of the firing rate r are modeled by an intrinsically noisy OU process described by equation (16) with parameter values listed in Appendix 3. (A) Intrinsic noise amplitude is set to \(\eta= 2\). Dual homeostasis converges on a fixed point near the fixed point of the corresponding system with no intrinsic noise, illustrated in Fig. 1A-D. (B) Firing rate mean \(\langle r \rangle\) and variance \(\operatorname{var}(r)\) are calculated and displayed as functions of x and g in x/g parameter space. The fixed point of the system is marked in white. (C) Intrinsic noise amplitude is set to \(\eta= 10\). Dual homeostasis fails to converge: x winds up without bound, and g winds down toward zero. (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