Stochastic resonance on paced genetic regulatory small-world networks: effects of asymmetric potentials |
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Authors: | M Perc |
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Institution: | (1) Department of Physics, Faculty of Natural Sciences and Mathematics, University of Maribor Koroška cesta 160, 2000 Maribor, Slovenia |
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Abstract: | We study the phenomenon of stochastic resonance on
small-world networks consisting of bistable genetic regulatory units,
whereby the external subthreshold periodic forcing is introduced as a
pacemaker trying to impose its rhythm on the whole network through the
single unit to which it is introduced. Without the addition of additive
spatiotemporal noise, however, the whole network remains forever trapped 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
significantly on the asymmetry of the two potential wells characterizing the
bistable dynamics, which can be tuned via a single system parameter. In
particular, we show that the ratio between the clustering coefficient and
the characteristic path length is a suitable quantity defining the ability
of a small-world network to facilitate the outreach of the pacemaker-emitted
subthreshold rhythm, but only if the asymmetry between the potentials is
practically negligible. In case of substantially asymmetric potentials the
impact of the small-world topology is less profound and cannot warrant an
enhancement of stochastic resonance by units that are located far from the
pacemaker. |
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Keywords: | PACS" target="_blank">PACS 05 40 -a Fluctuation phenomena random processes noise and Brownian motion 05 45 -a Nonlinear dynamics and chaos 87 16 A- Theory modeling and simulations 89 75 Hc Networks and genealogical trees |
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