Dynamic characterization of coupled nonlinear oscillators caused by the instability of ionization waves

Fukuyama, Tokihiko; Okugawa, M.

doi:10.1063/1.4977804

Cited by 9 publications

(3 citation statements)

References 25 publications

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“…A system involving ionization waves in a discharge tube has degree of freedom in time and space, and time- series signals are obtained from fluctuations in the light intensity by using photodiodes and a line-scan camera. In our previous works [13,17], only time-series data for the analysis were sampled using a photodiode. Moreover, in this study, data corresponding to the spatial position is sampled simultaneously using a line-scan camera, where time-series signals are obtained every 35.0 µs and the spatial data are obtained as the fluctuations in the light intensity.…”

Section: Resultsmentioning

confidence: 99%

Spatiotemporal Structure of Ionization Waves in a Glow Discharge Plasma

Fukuyama

Ishida

Kanzaki

2019

Plasma and Fusion Research

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Spatiotemporal structures formed in ionization waves are experimentally investigated in this study. A system involving ionization waves in a discharge tube has a few degrees of freedom in time and space. In our experiment, neon plasma is produced in a glass tube by a glow discharge between electrodes after the tube is evacuated to form a high vacuum. Spatiotemporal signals for the analysis are sampled as fluctuations in the light intensity by using a line-scan camera and photodiodes. The largest Lyapunov exponents are calculated from the time-series data sampled from the line-scan camera and photodiodes. Reconnection in the spatiotemporal structure is observed, which is caused by Eckhaus instability. Topological defects in the spatiotemporal structure are observed, which result in the appearance of spatiotemporal chaos; this leads to an order structure when an electric pulse is applied to the system as an external force or when coupled oscillators are synchronized.

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Section: Resultsmentioning

confidence: 99%

Spatiotemporal Structure of Ionization Waves in a Glow Discharge Plasma

Fukuyama

Ishida

Kanzaki

2019

Plasma and Fusion Research

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“…Routes to chaos through intermittency [8] have been extensively studied from both theoretical and experimental perspectives, in addition to routes to chaos through period-doubling bifurcations [10] and quasi-periodicity [11]. Chaos control and synchronization of coupled nonlinear oscillators are popular topics in nonlinear physics [12][13][14][15][16][17][18][19][20][21][22][23][24][25]. The time-delayed auto-synchronization method [15], a control method for chaos, has been widely used in experimental systems [18] because it is versatile and noise resistant.…”

Section: Introductionmentioning

confidence: 99%

Observation of Intermittent Chaos Caused by Delayed Feedback in a Laboratory Plasma

FUKUYAMA,

SUEYOSHI

2023

Plasma and Fusion Research

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In this study, experimental investigation was conducted on intermittent chaos caused by time-delayed feedback in the laboratory plasma. In a limit cycle with time-delayed feedback, a periodic system moved down the intermittency route to chaos, with the appearance of an increasing number of bursts that interfered with the laminar flow, as the feedback signal strength increased if an appropriate delay time was not selected. Analyses of the obtained time series revealed that the system with feedback has chaotic characteristics and that the shape of the recurrence plot differs from that of the turbulent state in which feedback is not applied. By observing the spatiotemporal structure, it was revealed that the system, which is in a periodic state both in time and space, transitions to a state of spatiotemporal chaos through the application of feedback. In this study, it was observed that the system undergoes intermittency, which leads to a chaotic state when time-delayed feedback is provided to nonlinear limit-cycle oscillations. c

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“…Although ecologists have long been interested in understanding large assemblages of interacting species, relatively little research in ecology has drawn on the body of theory associated with coupled oscillators. In many branches of science the issue of coupled oscillators is a key metaphor for developing general theory, from electronics to neurobiology (Norton et al, 2018;Laing, 2017;Fukuyama, and Okugawa, 2017).…”

Section: Introductionmentioning

confidence: 99%

Viewing communities as coupled oscillators: elementary forms from Lotka and Volterra to Kuramoto

Hajian‐Forooshani

Vandermeer

2020

Preprint

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Ecosystems and their embedded ecological communities are almost always by definition collections of oscillating populations. This is apparent given the qualitative reality that oscillations emerge from consumer-resource interactions, which are the simple building blocks for ecological communities. It is also likely always the case that oscillatory consumer-resource pairs will be connected to one another via trophic cross-feeding with shared resources or via competitive interactions among resources. Thus, one approach to understanding the dynamics of communities conceptualizes them as collections of oscillators coupled in various arrangements. Here we look to the pioneering work of Kuramoto on coupled oscillators and ask to what extent can his insights and approaches be translated to ecological systems. We explore all possible coupling arrangements of the simple case of three oscillator systems with both the Kuramoto model and with the classical Lotka-Volterra equations that are foundational to ecology. Our results show that the six-dimensional analogous Lotka-Volterra systems behave strikingly similarly to that of the corresponding Kuramoto systems across all possible coupling combinations. This qualitative similarity in the results between these two approaches suggests that a vast literature on coupled oscillators that has largely been ignored by ecologists may in fact be relevant in furthering our understanding of ecosystem and community organization.

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Dynamic characterization of coupled nonlinear oscillators caused by the instability of ionization waves

Cited by 9 publications

References 25 publications

Spatiotemporal Structure of Ionization Waves in a Glow Discharge Plasma

Spatiotemporal Structure of Ionization Waves in a Glow Discharge Plasma

Observation of Intermittent Chaos Caused by Delayed Feedback in a Laboratory Plasma

Viewing communities as coupled oscillators: elementary forms from Lotka and Volterra to Kuramoto

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