1. Spatial decoherence induced by small-world connectivity in excitable mediaMatjaž 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: 413
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2. Double resonance in cooperation induced by noise and network variation for an evolutionary prisoner's dilemmaMatjaž Perc, 2006, original scientific article Abstract: We study effects of slowly varying small-world topology and additive spatiotemporal random variations, introduced to the payoffs of a spatial prisoner's dilemma game, on the evolution of cooperation. We show that there exists an optimal fraction of shortcut links, constituting the variable complex network of participating players of the game, for which noise-induced cooperation is resonantly enhanced, thus marking a double resonance phenomenon in the studied system. The double resonance is attributed to the time-dependence of the connectivity structure that induces a tendency towards the mean-field behaviour in the limit of random graphs. We argue that random payoff disturbances and complex network topology are two potent extrinsic factors able to boost cooperation, thus representing a viable escape hatch out of evolutionary stalemate.
Keywords: dynamic systems, noise, spatiotemporal noise, intensity, spatial resonance, inherent spatial resonance, prisoner's dilemma
Published in DKUM: 07.06.2012; Views: 1769; Downloads: 422
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3. Evolutionary and dynamical coherence resonances in the pair approximated prisoner's dilemma gameMatjaž 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: 410
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4. Coherence resonance in a spatial prisoner's dilemma gameMatjaž 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: 465
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5. Proximity to periodic windows in bifurcation diagrams as a gateway to coherence resonance in chaotic systemsMarko Gosak, Matjaž Perc, 2007, original scientific article Abstract: We show that chaotic states situated in the proximity of periodic windows in bifurcation diagrams are eligible for the observation of coherence resonance. In particular, additive Gaussian noise of appropriate intensity can enhance the temporal order in such chaotic states in a resonant manner. Results obtained for the logistic map and the Lorenz equations suggest that the presented mechanism of coherence resonance is valid beyond particularities of individual systems. We attribute the findings to the increasing attraction of imminent periodic orbits and the ability of noise to anticipate their existence and use a modified wavelet analysis to support our arguments.
Keywords: chaotic systems, spatial resonance, coherence resonance, nonlinear systems, noise, spatial dynamics, mathematical models, bifurcation diagrame
Published in DKUM: 07.06.2012; Views: 2407; Downloads: 143
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6. Spatial coherence resonance in excitable biochemical media induced by internal noiseMarko Gosak, Marko Marhl, Matjaž Perc, 2007, original scientific article Abstract: We show that in a spatially extended excitable medium, presently modelled with diffusively coupled FitzHugh-Nagumo neurons, internal stochasticity is able to extract a characteristic spatial frequency of waves on the spatial grid. Internal noise is introduced via a stochastic simulation method and is the only agent acting on the system. Remarkably, the spatial periodicity is best pronounced at an intermediate level of internal stochasticity. Thus, the reported phenomenon is an observation of internal noise spatial coherence resonance in excitable biochemical media.
Keywords: noise, spatiotemporal noise, intensity, spatial resonance, spatial coherence resonance, excitable media, excitable biochemical media, neuronal dynamics, internal noise
Published in DKUM: 07.06.2012; Views: 1735; Downloads: 85
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7. Periodic calcium waves in coupled cells induced by internal noiseMatjaž Perc, Marko Gosak, Marko Marhl, 2007, original scientific article Abstract: We show that internal stochasticity, originating from finite cell sizes and related small numbers of reactant ions participating in the dynamics, is able to extract a characteristic spatial frequency of calcium waves in the medium of diffusively coupled cells. Internal noise is thereby the only agent acting on the system. As the spatial periodicity is best pronounced at an intermediate level of stochasticity the reported phenomenon is thus a novel observation of internal noise spatial coherence resonance in biochemical tissue-like media. In addition, results shed light on the stochastic versus deterministic nature of dynamics at the cellular and tissue level.
Keywords: noise, spatiotemporal noise, intensity, spatial resonance, chemical media, stochastic systems
Published in DKUM: 07.06.2012; Views: 1816; Downloads: 93
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8. Transition from Gaussian to Levy distributions of stochastic payoff variations in the spatial prisoner's dilemma gameMatjaž Perc, 2007, original scientific article Abstract: We study the impact of stochastic payoff variations with different distributions on the evolution of cooperation in the spatial prisoner's dilemma game. We find that Gaussian-distributed payoff variations are most successful in promoting cooperation irrespective of the temptation to defect. In particular, the facilitative effect of noise on the evolution of cooperation decreases steadily as the frequency of rare events increases. Findings are explained via an analysis of local payoff ranking violations. The relevance of results for economics and sociology is discussed.
Keywords: stochastic systems, spatial resonance, stochastic payoff variations, nonlinear systems, noise, spatial dynamics, mathematical models, prisoner's dilemma
Published in DKUM: 07.06.2012; Views: 2122; Downloads: 110
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9. Spatial coherence resonance in neuronal media with discrete local dynamicsMatjaž Perc, 2006, original scientific article Abstract: We study effects of spatiotemporal additive noise on the spatial dynamics of excitable neuronal media that is locally modelled by a two-dimensional map. We focus on the ability of noise to enhance a particular spatial frequency of the media in a resonant manner. We show that there exists an optimal noise intensity for which the inherent spatial periodicity of the media is resonantly pronounced, thus marking the existence of spatial coherence resonance in the studied system. Additionally, results are discussed in view of their possible biological importance.
Keywords: physics, complex systems, dynamical systems, noise, spatial dynamics, chaos, chaotic systems, chaos control, resonance
Published in DKUM: 07.06.2012; Views: 2462; Downloads: 108
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