Journal Article•
Pattern Dynamics in a Two-Dimensional Gas Discharge System(Oscillation, Chaos and Network Dynamics in Nonlinear Science)
About: This article is published in Progress of Theoretical Physics Supplement.The article was published on 2006-04-20 and is currently open access. It has received 3 citations till now. The article focuses on the topics: Oscillation & Network dynamics.
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TL;DR: In this paper, a qualitative analysis of dissipative structures in planar low-temperature dc gas-discharge devices with a high ohmic barrier is presented, and it is demonstrated that for these systems a deep qualitative understanding can be obtained from the point of view of synergetics.
Abstract: The understanding of self-organized patterns in spatially extended nonlinear dissipative systems is one of the most challenging subjects in modern natural sciences. Such patterns are also referred to as dissipative structures. We review this phenomenon in planar low temperature dc gas-discharge devices with a high ohmic barrier. It is demonstrated that for these systems a deep qualitative understanding of dissipative structures can be obtained from the point of view of synergetics. At the same time, a major contribution can be made to the general understanding of dissipative structures. The discharge spaces of the experimentally investigated systems, to good approximation, have translational and rotational symmetry by contraction. Nevertheless, a given system may exhibit stable current density distributions and related patterns that break these symmetries. Among the experimentally observed fundamental patterns one finds homogeneous isotropic states, fronts, periodic patterns, labyrinth structures, rotating spirals, target patterns and localized filaments. In addition, structures are observed that have the former as elementary building blocks. Finally, defect structures as well as irregular patterns are common phenomena. Such structures have been detected in numerous other driven nonlinear dissipative systems, as there are ac gas-discharge devices, semiconductors, chemical solutions, electrical networks and biological systems. Therefore, from the experimental observations it is concluded that the patterns in planar low temperature dc gas-discharge devices exhibit universal behavior. From the theoretical point of view, dissipative structures of the aforementioned kind are also referred to as attractors. The possible sets of attractors are an important characteristic of the system. The number and/or qualitative nature of attractors may change when changing parameters. The related bifurcation behavior is a central issue of the synergetic approach chosen in the present article. A short review of possible theoretical approaches reveals that a theoretical description of the experimentally observed patterns is far from being satisfactory. Bearing this in mind, a qualitative model of the reaction-diffusion type is considered. Surprisingly enough, this model allows for a qualitative description of almost all fundamental patterns that have been observed experimentally. Also, so far the predictive power of this model is unmatched.
142 citations
TL;DR: The main issue is to study the collision dynamics between traveling pulses and defects, and show that their global bifurcation structure plays a key role in clarifying the underlying mechanism.
Abstract: We consider the dynamics when traveling pulses encounter heterogeneities in a three-component reaction diffusion system of one-activator-two-inhibitor type, which typically arises as a qualitative model of a gas-discharge system. We focused on the case where one of the kinetic coefficients changes similar to a smoothed step function, which is basic for more general heterogeneity as in periodic or random media. Since the heterogeneity is introduced to the kinetic part in an additive way, it causes the system to produce various types of localized structures smoothing the jump heterogeneity called the defects at the jump point, which makes a sharp contrast with the multiplicative heterogeneous case for the Gray-Scott model. The main issue is to study the collision dynamics between traveling pulses and defects, and show that their global bifurcation structure plays a key role in clarifying the underlying mechanism. Five outputs are observed after collisions including annihilation, rebound, and pinning. Unstable steady states are identified as separators between two different dynamic regimes: penetration and rebound, the role of which is very close to that of scattors arising in collision process. An organizing center producing the traveling pulses, defects, and scattors via unfolding with respect to the parameters is also presented.
51 citations
TL;DR: The results suggest that subjects’ attentional states are associated with distinct spatio-temporal patterns of the phase-locked clusters of the global phase-synchrony, and confirm the existence of stable phase- Synchronized clusters.
Abstract: It has been discussed that neural phase-synchrony across distant cortical areas (or global phase-synchrony) was correlated with various aspects of consciousness. The generating process of the synchrony, however, remains largely unknown. As a first step, we investigate transient process of global phase-synchrony, focusing on phase-synchronized clusters. We hypothesize that the phase-synchronized clusters are dynamically organized before global synchrony and clustering patterns depend on perceptual conditions. In an EEG study, Kitajo reported that phase-synchrony across distant cortical areas was selectively enhanced by top-down attention around 4 Hz in Necker cube perception. Here, we further analyzed the phase-synchronized clusters using hierarchical clustering which sequentially binds up the nearest electrodes based on similarity of phase locking between the cortical signals. First, we classified dominant components of the phase-synchronized clusters over time. We then investigated how the phase-synchronized clusters change with time, focusing on their size and spatial structure. Phase-locked clusters organized a stable spatial pattern common to the perceptual conditions. In addition, the phase-locked clusters were modulated transiently depending on the perceptual conditions and the time from the perceptual switch. When top-down attention succeeded in switching perception as subjects intended, independent clusters at frontal and occipital areas grew to connect with each other around the time of the perceptual switch. However, the clusters in the occipital and left parietal areas remained divided when top-down attention failed in switching perception. When no primary biases exist, the cluster in the occipital area grew to its maximum at the time of the perceptual switch within the occipital area. Our study confirmed the existence of stable phase-synchronized clusters. Furthermore, these clusters were transiently connected with each other. The connecting pattern depended on subjects’ internal states. These results suggest that subjects’ attentional states are associated with distinct spatio-temporal patterns of the phase-locked clusters.
14 citations
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