Superlinearly scalable noise robustness of redundant coupled dynamical systems

Abstract

We illustrate through theory and numerical simulations that redundant coupled dynamical systems can be extremely robust against local noise in comparison to uncoupled dynamical systems evolving in the same noisy environment. Previous studies have shown that the noise robustness of redundant coupled dynamical systems is linearly scalable and deviations due to noise can be minimized by increasing the number of coupled units. Here, we demonstrate that the noise robustness can actually be scaled superlinearly if some conditions are met and very high noise robustness can be realized with very few coupled units. We discuss these conditions and show that this superlinear scalability depends on the nonlinearity of the individual dynamical units. The phenomenon is demonstrated in discrete as well as continuous dynamical systems. This superlinear scalability not only provides us an opportunity to exploit the nonlinearity of physical systems without being bogged down by noise but may also help us in understanding the functional role of coupled redundancy found in many biological systems. Moreover, engineers can exploit superlinear noise suppression by starting a coupled system near (not necessarily at) the appropriate initial condition.

Implementing Boolean Functions in Hybrid Digital-Analog Systems

“…The output is then decoded using a simple threshold detecting decoder. This architecture is robust to noise as the effect of noise is minimum at super-stable initial conditions and can scale superlinearly by coupling redundant circuits [11]. Moreover, if the domain and codomain of the nonlinear circuit are same, then the output can be used directly as an input to the next stage, allowing an easy concatenation of CC elements.…”

“…If d dx (f i (x 0 )) = 0, then the second term will be zero and the difference between f i (x 0 ) and f i (x 0 + δ) is proportional to higher order terms which are very close to zero if δ is small. So, the super-stable initial conditions of the nonlinear circuit are robust against perturbations [11] and map to maxima and minima of the response function of the nonlinear circuit.…”

“…The number of implementable functions increases exponentially with the number of iterations [5], so it is crucial that we can maximize the iterations for which output can be obtained successfully. One method to achieve this objective is to suppress the noise evolution through coupled redundant nonlinear circuits as the local noise in different circuits averages out and the overall deviation in the output is reduced [9][10][11].…”