How Synchronization Protects from Noise

Abstract

The functional role of synchronization has attracted much interest and debate: in particular, synchronization may allow distant sites in the brain to communicate and cooperate with each other, and therefore may play a role in temporal binding, in attention or in sensory-motor integration mechanisms. In this article, we study another role for synchronization: the so-called “collective enhancement of precision”. We argue, in a full nonlinear dynamical context, that synchronization may help protect interconnected neurons from the influence of random perturbations—intrinsic neuronal noise—which affect all neurons in the nervous system. More precisely, our main contribution is a mathematical proof that, under specific, quantified conditions, the impact of noise on individual interconnected systems and on their spatial mean can essentially be cancelled through synchronization. This property then allows reliable computations to be carried out even in the presence of significant noise (as experimentally found e.g., in retinal ganglion cells in primates). This in turn is key to obtaining meaningful downstream signals, whether in terms of precisely-timed interaction (temporal coding), population coding, or frequency coding. Similar concepts may be applicable to questions of noise and variability in systems biology.

Stabilizing Quorum-Sensing Networks via Noise

“…In fact, from (5) it is straightforward to see that the higher the number of nodes ism the higher the noise intensity σ * needs to be in order to drive the state of all the network nodes to 0. In this sense, nodes are cooperating to protect the network from noise and this is similar in spirit to a recent result presented in [11]. Finally, we discuss here some possible generalizations of the result presented in this paper, which will be presented elsewhere: (i) the quorum sensing dynamics studied in this paper has been obtained under the assumption that the dynamics of the shared variable is sufficiently fast.…”

“…This is surprising as such networks, besides their pervasiveness in Nature, could also be used in designing engineered network systems with the goal of minimizing the number of node-tonode links, while achieving some desired connectivity level [11]. Recently, a large body of Literature is emerging on the study of synchronization effects in the presence of noise, see e.g., [12], [1].…”

Control principles of complex systems

“…To obtain a sufficient condition, one can use global stability analysis, like Lyapunov's direct method (Belykh et al, 2006(Belykh et al, , 2005(Belykh et al, , 2004aChen, 2006Chen, , 2008Li et al, 2009;Chua, 1994, 1995a,b,c) or contraction theory (Aminzare and Sontag, 2015;Li et al, 2007;Lohmiller and Slotine, 1998;Pham and Slotine, 2007;Russo and Di Bernardo, 2009;Tabareau et al, 2010;Wang and Slotine, 2005).…”

How to desynchronize quorum-sensing networks

“…Literature devoted to the study of the emerging behaviors in quorum sensing networks (e.g., [19], [20], [21], [22]) is sparse when compared to that on diffusive topologies. Moreover, in some cases, results are obtained by neglecting the dynamics of the quorum/environmental variables, as well as the global effects of nonlinearities.…”