1. 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: 135
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2. 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: 83
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3. 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: 108
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4. 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: 106
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