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Spatial decoherence induced by small-world connectivity in excitable media
Matjaž Perc, 2005, original scientific article

Abstract: We study effects of different network topologies on the noise-induced pattern formation in a two-dimensional model of excitable media with FitzHugh-Nagumo local dynamics. In particular, we show that the introduction of long-range couplings induces decoherence of otherwise coherent noise-induced spatial patterns that can be observed by regular connectivity of spatial units. Importantly, already a small fraction of long-range couplings is sufficient to destroy coherent pattern formation. We argue that the small-world network topology destroys spatial order due to the lack of a precise internal spatial scale, which by regular connectivity is given by the coupling constant and the noise robust excursion time that is characteristic for the local dynamics. Additionally, the importance of spatially versus temporally ordered neural network functioning is discussed.
Keywords: dynamic systems, noise, spatiotemporal noise, intensity, spatial resonance, inherent spatial resonance, spatial decoherence, excitable media
Published in DKUM: 07.06.2012; Views: 1537; Downloads: 403
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Evolutionary and dynamical coherence resonances in the pair approximated prisoner's dilemma game
Matjaž Perc, Marko Marhl, 2006, original scientific article

Abstract: Stochasticity has recently emerged as being a potent promoter of cooperative behaviour in systems developed under the framework of evolutionary game theory. In the spatial prisoner's dilemma game, the fitness of players adopting the cooperative strategy was found to be resonantly dependent on the intensity of payoff fluctuations. Evidently, the phenomenon resembles classical coherence resonance, whereby the noise-induced order, or coherence, of the dynamics is substituted with the noise-induced prevalence of the 'good' strategy, thus marking a constructive effect of noise on the system. The connection between the former 'dynamical' coherence resonance and the latter so-called 'evolutionary' coherence resonance, however, has not yet been established. The two different definitions of coherence resonance appear to provoke some discomfort. The goal of the present paper is therefore, on one hand, to draw a clear line between the two different perceptions of coherence resonance, and on the other, to show that the two apparently disjoint phenomena, that are currently related only by name, can in fact be observed simultaneously, sharing an identical mechanism of emergence.
Keywords: dynamic systems, noise, spatiotemporal noise, intensity, spatial resonance, inherent spatial resonance, spatial decoherence, excitable media
Published in DKUM: 07.06.2012; Views: 2340; Downloads: 401
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Coherence resonance in a spatial prisoner's dilemma game
Matjaž Perc, 2006, original scientific article

Abstract: We study effects of additive spatiotemporal random variations, introduced to the payoffs of a spatial prisoner's dilemma game, on the evolution of cooperation. In the absence of explicit payoff variations the system exhibits a phase transition from a mixed state of cooperators and defectors to a homogenous state of defectors belonging to the directed percolation universality class. By introducing nonzero random variations to the payoffs, this phase transition can be reverted in a resonance-like manner depending on the variance of noise, thus marking coherence resonance in the system. We argue that explicit random payoff variations present a viable mechanism that promotes cooperation for defection temptation values substantially exceeding the one marking the transition point to homogeneity by deterministic payoffs.
Keywords: dynamic systems, noise, spatiotemporal noise, intensity, spatial resonance, inherent spatial resonance, spatial decoherence, excitable media
Published in DKUM: 07.06.2012; Views: 1732; Downloads: 449
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