Chemical Oscillations, Waves, and Turbulence

Kuramoto, Yoshio

doi:10.1007/978-3-642-69689-3

Cited by 6,238 publications

(7,191 citation statements)

References 73 publications

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“…Using the theory of weakly coupled oscillators (Kuramoto 1984;Malkin 1949;Ermentrout 1984), the dynamics of the HCO can be reduced to the consideration of a "phase model", in which the state of the oscillator is described entirely by its phase θ(t). The phase can be decomposed into two parts: θ(t) = t + φ(t) mod T , where t describes the change in the phase of the oscillator in the absence of the external input, and the relative phase φ(t) quantifies the phase shift that results from the external input.…”

Section: Phase Modelsmentioning

confidence: 99%

Phase response properties of half-center oscillators

Zhang

Lewis

2013

J Comput Neurosci

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We examine the phase response properties of half-center oscillators (HCOs) that are modeled by a pair of Morris-Lecar-type neurons connected by strong fast inhibitory synapses. We find that the two basic mechanisms for half-center oscillations, "release" and "escape", give rise to strikingly different phase response curves (PRCs). Release-type HCOs are most sensitive to perturbations delivered to cells at times when they are about to transition from the active to the suppressed state, and PRCs are dominated by a large negative peak (phase delays) at corresponding phases. On the other hand, escape-type HCOs are most sensitive to perturbations delivered to cells at times when they are about to transition from the suppressed to the active state, and PRCs are dominated by a large positive peak (phase advances) at corresponding phases. By analyzing the phase space structure of Morris-Lecar-type HCO models with fast synaptic dynamics, we identify the dynamical mechanisms underlying the shapes of the PRCs. To demonstrate the significance of the different shapes of the PRCs for the release-type and escape-type HCOs, we link the shapes of the PRCs to the different frequency modulation properties of release-type

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Section: Phase Modelsmentioning

confidence: 99%

Phase response properties of half-center oscillators

Zhang

Lewis

2013

J Comput Neurosci

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“…Under the assumption that the coupling functions G i are weak and the oscillatory dynamics are harmonic [Kuramoto, 1984], the above equations can be reduced to a simpler set written in terms of the oscillators' phase angles θ i asθ…”

Section: Model Of Two Coupled Oscillatorsmentioning

confidence: 99%

“…It is also known as the classical Kuramoto model [Kuramoto, 1984], where K is the coupling gain between the oscillators. It is assumed to be isotropic for both oscillators.…”

Section: Extending the Kuramoto Modelmentioning

confidence: 99%

Modeling inter-human movement coordination: synchronization governs joint task dynamics

et al. 2012

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Human interaction partners tend to synchronize their movements during repetitive actions such as walking. Research of inter-human coordination in purely rhythmic action tasks reveals that the observed patterns of interaction are dominated by synchronization effects. Initiated by our finding that human dyads synchronize their arm movements even in a goal-directed action task, we present a step-wise approach to a model of inter-human movement coordination. In an experiment, the hand trajectories of ten human dyads are recorded. Governed by a dynamical process of phase synchronization, the participants establish in-phase as well as anti-phase relations. The emerging relations are successfully reproduced by the attractor dynamics of coupled phase oscillators inspired by the Kuramoto model. Three different methods on transforming the motion trajectories into instantaneous phases are investigated and their influence on the model fit to the experimental data is evaluated. System identification technique allows us to estimate the model parameters, which are the coupling strength and the frequency detuning among the dyad. The stability properties of the identified model match the relations observed in the experimental data. In short, our model predicts the dynamics of inter-human movement coordination. It can directly be implemented to enrich human-robot interaction.

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“…It is a well known fact (see, e.g. Malkin, 1949Malkin, , 1956Blechman, 1971;Neu, 1979;Ermentrout, 1981;Kuramoto, 1984;Ermentrout and Kopell, 1991) that the entire system (1, 2) can be approximated by a phase model that is defined on the n+ 1 dimensional torus T n + 1 . Hoppensteadt and Izhikevich (1997) have gone further and proved that there is actually a continuous change of variables that transforms (1, 2) into the phase model.…”

Section: Autonomous Oscillationsmentioning

confidence: 99%

Thalamo-cortical interactions modeled by weakly connected oscillators: could the brain use FM radio principles?

1998

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We consider all models of the thalamo-cortical system that satisfy the following two assumptions: (1) each cortical column is an autonomous oscillator; (2) connections between cortical columns and the thalamus are weak. Our goal is to deduce from these assumptions general principles of thalamo-cortical interactions that are independent of the equations describing the system. We find that the existence of synaptic connections between any two cortical columns does not guarantee that the columns interact: They interact only when there is a certain nearly resonant relation between their frequencies, which implies that the interactions are frequency modulated (FM). When the resonance relation holds, the cortical columns interact through phase modulations. Thus, communications between weakly connected cortical oscillators employ a principle similar to that in FM radio: The frequency of oscillation encodes the channel of communication, while the information is transmitted via phase modulations. If the thalamic input has an appropriate frequency, then it can dynamically link any two cortical columns, even those that have non-resonant frequencies and would otherwise be unlinked. Thus, by adjusting its temporal activity, the thalamus has control over information processing taking place in the cortex. Our results suggest that the mean firing rate (frequency) of periodically spiking neuron does not carry any information other than identifying a channel of communication. Information (i.e. neural code) is carried through modulations of interspike intervals.

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Chemical Oscillations, Waves, and Turbulence

Cited by 6,238 publications

References 73 publications

Phase response properties of half-center oscillators

Phase response properties of half-center oscillators

Modeling inter-human movement coordination: synchronization governs joint task dynamics

Thalamo-cortical interactions modeled by weakly connected oscillators: could the brain use FM radio principles?

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