Effect of Phase Response Curve Skewness on Synchronization of Electrically Coupled Neuronal Oscillators

We investigate why electrically coupled neuronal oscillators synchronize or fail to synchronize using the theory of weakly coupled oscillators. Stability of synchrony and antisynchrony is predicted analytically and verified using numerical bifurcation diagrams. The shape of the phase response curve (PRC), the shape of the voltage time course, and the frequency of spiking are freely varied to map out regions of parameter spaces that hold stable solutions. We find that type 1 and type 2 PRCs can hold both synchronous and antisynchronous solutions, but the shape of the PRC and the voltage determine the extent of their stability. This is achieved by introducing a five-piecewise linear model to the PRC and a three-piecewise linear model to the voltage time course, and then analyzing the resultant eigenvalue equations that determine the stability of the phase-locked solutions. A single time parameter defines the skewness of the PRC, and another single time parameter defines the spike width and frequency. Our approach gives a comprehensive picture of the relation of the PRC shape, voltage time course, and stability of the resultant synchronous and antisynchronous solutions.

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Temperature Sensitive Events between Photoreceptor and Circadian Clock?

Zeitschrift für Naturforschung C ◽

10.1515/znc-1975-3-416 ◽

1975 ◽

Vol 30 (3-4) ◽

pp. 240-244 ◽

Cited By ~ 12

Author(s):

Ursula Hamm ◽

M Aroli ◽

K Chandrashekaran ◽

W Olfgang Engelmann

Keyword(s):

Low Temperature ◽

Response Curve ◽

Time Course ◽

Phase Response Curve ◽

Phase Response ◽

Phase Shifting ◽

Wave Form ◽

Temperature Sensitive ◽

Slowing Down ◽

Light Pulses

Abstract The phase shifting action of low temperature pulses of 6 °C and 2 h duration administered to the various phases of the Drosophila pseudoobscura circadian rhythm and the action of light pulses given 30 min after the beginning of these low temperature pulses have been investigated. The phase response curve obtained from experiments with light pulses during low temperature cannot be ex plained on the basis of a straightforward and sequential phase shifting of the oscillation by the various transitions in the pulses. The response curve, after the slight phase shifting action of the temperature pulses is corrected for, resembles the standard phase response curve 4 for light pulses (at 20 °C) in its wave form but not in its time course. Our curve is shifted in time in a manner that indicates that the light pulses accompanying the low temperature pulses arrived at phase points 1.5 h later than the actual phases at which they were given. We attribute this delay to a slowing down of the information that is apparently transmitted by a process that is temperature dependent.

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Effect of Phase Response Curve Shape and Synaptic Driving Force on Synchronization of Coupled Neuronal Oscillators

Neural Computation ◽

10.1162/neco_a_00978 ◽

2017 ◽

Vol 29 (7) ◽

pp. 1769-1814 ◽

Cited By ~ 2

Author(s):

Ramana Dodla ◽

Charles J. Wilson

Keyword(s):

Response Curve ◽

Phase Response Curve ◽

Reversal Potential ◽

Phase Response ◽

Neuron Models ◽

Integrate And Fire ◽

Weakly Coupled ◽

Neuronal Oscillators ◽

The Stability ◽

Voltage Spike

The role of the phase response curve (PRC) shape on the synchrony of synaptically coupled oscillating neurons is examined. If the PRC is independent of the phase, because of the synaptic form of the coupling, synchrony is found to be stable for both excitatory and inhibitory coupling at all rates, whereas the antisynchrony becomes stable at low rates. A faster synaptic rise helps extend the stability of antisynchrony to higher rates. If the PRC is not constant but has a profile like that of a leaky integrate-and-fire model, then, in contrast to the earlier reports that did not include the voltage effects, mutual excitation could lead to stable synchrony provided the synaptic reversal potential is below the voltage level the neuron would have reached in the absence of the interaction and threshold reset. This level is controlled by the applied current and the leakage parameters. Such synchrony is contingent on significant phase response (that would result, for example, by a sharp PRC jump) occurring during the synaptic rising phase. The rising phase, however, does not contribute significantly if it occurs before the voltage spike reaches its peak. Then a stable near-synchronous state can still exist between type 1 PRC neurons if the PRC shows a left skewness in its shape. These results are examined comprehensively using perfect integrate-and-fire, leaky integrate-and-fire, and skewed PRC shapes under the assumption of the weakly coupled oscillator theory applied to synaptically coupled neuron models.

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Piecewise linear model of self-organized hierarchy formation

Physical Review E ◽

10.1103/physreve.102.032213 ◽

2020 ◽

Vol 102 (3) ◽

Author(s):

Tomoshige Miyaguchi ◽

Takamasa Miki ◽

Ryota Hamada

Keyword(s):

Linear Model ◽

Piecewise Linear ◽

Self Organized ◽

Piecewise Linear Model ◽

Hierarchy Formation

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Model of bidirectional interaction between myocardial pacemakers based on the phase response curve

Biological Cybernetics ◽

10.1007/bf00319975 ◽

1982 ◽

Vol 43 (3) ◽

pp. 157-167 ◽

Cited By ~ 30

Author(s):

Noriaki Ikeda

Keyword(s):

Response Curve ◽

Phase Response Curve ◽

Phase Response

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Effect of Mean Stress on the Fatigue Life Prediction of Notched Fiber-Reinforced 2060 Al-Li Alloy Laminates under Spectrum Loading

Advances in Materials Science and Engineering ◽

10.1155/2018/5728174 ◽

2018 ◽

Vol 2018 ◽

pp. 1-16

Author(s):

Weiying Meng ◽

Liyang Xie ◽

Yu Zhang ◽

Yawen Wang ◽

Xiaofang Sun ◽

...

Keyword(s):

Fatigue Life ◽

Linear Model ◽

Life Prediction ◽

Piecewise Linear ◽

Forecast Accuracy ◽

Cyclic Stress ◽

Fatigue Life Prediction ◽

Fiber Reinforced ◽

Piecewise Linear Model ◽

Spectrum Loading

This paper presents a study on the fatigue life prediction of notched fiber-reinforced 2060 Al-Li alloy laminates under spectrum loading by applying the constant life diagram. Firstly, a review on the state of the art of constant life diagram models for the life prediction of composite materials is given, which highlights the effect on the forecast accuracy. Then, the fatigue life of notched fiber-reinforced Al-Li alloy laminates (2/1 laminates and 3/2 laminates) is tested under cyclic stress, which has different stress cycle characteristics (constant amplitude loading and Mini-Twist spectrum loading). The introduced models are successfully realized based on the available experimental data of examined laminates. In the case of Mini-Twist spectrum loading, the effect of the constant life diagram on the life prediction accuracy of examined laminates is studied based on the rainflow-counting method and Miner damage criteria. The results show that the simple Goodman model and piecewise linear model have certain advantages compared to other complex models for the life prediction of notched fiber metal laminates with different structures under Mini-Twist loading. From the engineering perspective, the S-N curve prediction based on the piecewise linear model is most applicable and accurate among all the models.

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