Pacemaker-driven stochastic resonance on diffusive and complex networks of bistable oscillators

Matjaž Perc (Author), Marko Gosak (Author)

Abstract

We study the phenomenon of stochastic resonance on diffusive, small-world and scale-free networks consisting of bistable overdamped oscillators. Important thereby is the fact that the external subthreshold periodic forcing is introduced only to a single oscillator of the network. Hence, the forcing acts as a pacemaker trying to impose its rhythm on the whole network through the unit to which it is introduced. Without the addition of additive spatiotemporal noise, however, the whole network, including the unit that is directly exposed to the pacemaker, remains trapped forever in one of the two stable steady states of the local dynamics. We show that the correlation between the frequency of subthreshold pacemaker activity and the response of the network is resonantly dependent on the intensity of additive noise. The reported pacemaker-driven stochastic resonance depends most significantly on the coupling strength and the underlying network structure. Namely, the outreach of the pacemaker obeys the classic diffusion law in the case of nearest-neighbor interactions, thus being proportional to the square root of the coupling strength, whereas it becomes superdiffusive by an appropriate small-world or scale-free topology of the interaction network. In particular, the scale-free topology is identified as being optimal for the dissemination of localized rhythmic activity across the whole network. Also, we show that the ratio between the clustering coefficient and the characteristic path length is the crucial quantity defining the ability of a small-world network to facilitate the outreach of the pacemaker-emitted subthreshold rhythm. We additionally confirm these findings by using the FitzHugh-Nagumo excitable system as an alternative to the bistable overdamped oscillator.

Keywords

šum;bistabilna dinamika;stohastične simulacije;kompleksne mreže;noise;bistable dynamics;stochastic simulations;complex networks;

Data

Language:	English
Year of publishing:	2008
Typology:	1.01 - Original Scientific Article
Organization:	UM FNM - Faculty of Natural Sciences and Mathematics
UDC:	519.83:53
COBISS:	12323606
ISSN:	1367-2630
Views:	806
Downloads:	372
Average score:	0 (0 votes)
Metadata:

Other data

Secondary language:	Slovenian
Secondary keywords:	šum;bistabilna dinamika;stohastične simulacije;kompleksne mreže;
URN:	URN:SI:UM:
Type (COBISS):	Scientific work
Pages:	str. 053008-1-053008-21
Volume:	ǂVol. ǂ10
Issue:	ǂiss. ǂ5
Chronology:	2008
DOI:	10.1088/1367-2630/10/5/053008
ID:	1482745