We study a nonlinear Langevin equation describing the dynamic variable X(t), the mean field (order parameter) of a finite size complex network at criticality. The conditions under which the autocorrelation function of X shows any direct connection with criticality are discussed. We find that if the network is prepared in a state far from equilibrium, X(0)=1, the autocorrelation function is characterized by evident signs of critical slowing down as well as by significant aging effects, while the preparation X(0)=0 does not generate evident signs of criticality on X(t), in spite of the fact that the same initial state makes the fluctuating variable η(t)≡sgn(X(t)) yield significant aging effects. These latter effects arise because the dynamics of η(t) are directly dependent on crucial events, namely the re-crossings of the origin, which undergo a significant aging process with the preparation X(0)=0. The time scale dominated by temporal complexity, aging, and ergodicity breakdown of η(t) is properly evaluated by adopting the method of stochastic linearization which is used to explain the exponential-like behavior of the equilibrium autocorrelation function of X(t).

This study demonstrates that the nature of the variability files, chosen to drive the variable ventilator, had no effect on indices of gas exchange or respiratory mechanics in this model. A considerable overlap of the multifractal files existed. The potential to drive a variable ventilator using algorithm-derived files with multifractal characteristics, thereby eliminating the requirement to use physiologically-derived signals, is discussed.