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Pacemaker-driven stochastic resonance on diffusive and complex networks of bistable oscillators
Matjaž Perc, Marko Gosak, 2008, original scientific article

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: noise, bistable dynamics, stochastic simulations, complex networks
Published in DKUM: 03.07.2017; Views: 1076; Downloads: 407
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Noise-guided evolution within cyclical interactions
Matjaž Perc, Attila Szolnoki, 2007, original scientific article

Abstract: We study a stochastic predator-prey model on a square lattice, where each of the six species has two superior and two inferior partners. The invasion probabilities between species depend on the predator-prey pair and are supplemented by Gaussian noise. Conditions are identified that warrant the largest impact of noise on the evolutionary process, and the results of Monte Carlo simulations are qualitatively reproduced by a four-point cluster dynamical mean-field approximation. The observed noise-guided evolution is deeply routed in short-range spatial correlations, which is supported by simulations on other host lattice topologies. Our findings are conceptually related to the coherence resonance phenomenon in dynamical systems via the mechanism of threshold duality. We also show that the introduced concept of noise-guided evolution via the exploitation of threshold duality is not limited to predator-prey cyclical interactions, but may apply to models of evolutionary game theory as well, thus indicating its applicability in several different fields of research.
Keywords: dynamic systems, stochastic processes, cyclical interactions, evolutionary rules, flow simulations, Monte Carlo simulations
Published in DKUM: 07.06.2012; Views: 1845; Downloads: 380
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Spatio-temporal modelling explains the effect of reduced plasma membrane Ca[sup]2+[/sup] efflux on intracellular Ca[sup]2+[/sup] oscillations in hepatocytes
Marko Marhl, Marko Gosak, Matjaž Perc, C. Jane Dixon, Anne K. Green, 2008, original scientific article

Abstract: In many non-excitable eukaryotic cells, including hepatocytes, ▫$Ca^{2+}$▫ oscillations play a key role in intra- and intercellular signalling, thus regulating many cellular processes from fertilisation to death. Therefore, understanding the mechanisms underlying these oscillations, and consequently understanding how they may be regulated, is of great interest. In this paper, we study the influence of reduced ▫$Ca^{2+}$▫ plasma membrane efflux on ▫$Ca^{2+}$▫ oscillations in hepatocytes. Our previous experiments with carboxyeosin show that a reduced plasma membrane ▫$Ca^{2+}$▫ efflux increases the frequency of ▫$Ca^{2+}$▫ oscillations, but does not affect the duration of individual transients. This phenomenon can be best explained by taking into account not only the temporal,but also the spatial dynamics underlying the generation of ▫$Ca^{2+}$▫ oscillations in the cell. Here we divide the cell into a grid of elements and treat the ▫$Ca^{2+}$▫ dynamics as a spatio-temporal phenomenon. By converting an existing temporal model into a spatio-temporal one, we obtain theoretical predictions that are in much better agreement with the experimental observations.
Keywords: cellular signalling, calcium oscillations, intracellular oscilations, spatio-temporal dynamics, hepatocytes, stochastic simulations
Published in DKUM: 07.06.2012; Views: 1312; Downloads: 49
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