Phase noise in coupled oscillators: theory and experiment

1997 ◽  
Vol 45 (5) ◽  
pp. 604-615 ◽  
Author(s):  
Heng-Chia Chang ◽  
Xudong Cao ◽  
U.K. Mishra ◽  
R.A. York
Keyword(s):  
Phase Noise ◽  
Coupled Oscillators ◽  
Theory And Experiment

Effects of local oscillator frequency on intersegmental coordination in the lamprey locomotor CPG: theory and experiment

1996 ◽  
Vol 76 (6) ◽  
pp. 4094-4103 ◽  
Author(s):  
K. A. Sigvardt ◽  
T. L. Williams
Keyword(s):  
Coupled Oscillators ◽  
Intact Animal ◽  
Local Oscillator ◽  
Ventral Root ◽  
Phase Lag ◽  
Intersegmental Coordination ◽  
Glutamate Concentration ◽  
Phase Lags ◽  
Theory And Experiment

1. Experiments have been performed on in vitro preparations of lamprey spinal cord bathed in D-glutamate, which induces a pattern of activity recorded from ventral roots that is similar to that seen in the intact animal during swimming. The frequency of fictive swimming increases with increasing D-glutamate concentration, but intersegmental phase lag remains unaffected. 2. The effects on intersegmental phase lags of unequal activation of the rostral and caudal halves of a preparation were determined. Unequal activation was produced by placing a diffusion barrier in the middle of the chamber and perfusing the two halves with different concentrations of D-glutamate. 3. Within the rostral compartment, the phase lag increased from control when the rostral D-glutamate concentration was higher than the caudal concentration, and decreased from control when it was lower. By contrast, the phase lags within the caudal compartment did not depend on the ratio of D-glutamate concentration between the two compartments. 4. The frequency of the ventral root activity during differential activation was not significantly different from that of control experiments that had the same concentration as in the rostral compartment. 5. The results are discussed within the context of the mathematical analysis of chains of coupled oscillators by Kopell and Ermentrout and other current theories about the mechanisms of intersegmental coordination in the lamprey.

Karhunen-Loeve Decomposition for Reducing the Order and Monitoring the Dynamics of Coupled Oscillators

2001 ◽  
Author(s):  
Xianghong Ma ◽  
Alexander F. Vakakis ◽  
Lawrence A. Bergman
Keyword(s):  
Coupled Oscillators ◽  
Large Scale ◽  
Order Reduction ◽  
Mode Shapes ◽  
Flexible Systems ◽  
Higher Order Modes ◽  
Orthogonality Relations ◽  
Series Of Experiments ◽  
Theory And Experiment ◽  
Low Order

Abstract Karhunen-Loeve - KL modes are used to discretize the dynamics of a four-bay linear truss. This is achieved by defining global KL modal amplitudes and employing the orthogonality relations between KL modes that are inherent in the KL decomposition. It is found that the KL-based low-order models can capture satisfactory the transient dynamics of the truss, even when only a limited number of them is used for the order reduction. A comparison between the exact and low-order dynamics in the frequency domain reveals that the low-order models capture the leading resonances of the truss. A series of experiments with a practical three-bay truss is then performed to validate the theoretical KL decomposition. A comparison between theory and experiment indicates agreement between the predicted and realized dominant KL mode shapes, but less so in the higher order modes. The reasons for this discrepancy between theory and experiment are discussed, and possible applications of the KL-based order reduction to passive and active control of practical large-scale flexible systems are outlined.

scholarly journals From local resynchronization to global pattern recovery in the zebrafish segmentation clock

eLife ◽  
2021 ◽  
Vol 10 ◽  
Author(s):  
Koichiro Uriu ◽  
Bo-Kai Liao ◽  
Andrew C Oates ◽  
Luis G Morelli
Keyword(s):  
Gene Expression ◽  
Coupled Oscillators ◽  
Expression Patterns ◽  
Tissue Mechanics ◽  
Gene Expression Patterns ◽  
Global Pattern ◽  
Segmentation Clock ◽  
Model Combining ◽  
Local Synchronization ◽  
Theory And Experiment

Integrity of rhythmic spatial gene expression patterns in the vertebrate segmentation clock requires local synchronization between neighboring cells by Delta-Notch signaling and its inhibition causes defective segment boundaries. Whether deformation of the oscillating tissue complements local synchronization during patterning and segment formation is not understood. We combine theory and experiment to investigate this question in the zebrafish segmentation clock. We remove a Notch inhibitor, allowing resynchronization, and analyze embryonic segment recovery. We observe unexpected intermingling of normal and defective segments, and capture this with a new model combining coupled oscillators and tissue mechanics. Intermingled segments are explained in the theory by advection of persistent phase vortices of oscillators. Experimentally observed changes in recovery patterns are predicted in the theory by temporal changes in tissue length and cell advection pattern. Thus, segmental pattern recovery occurs at two length and time scales: rapid local synchronization between neighboring cells, and the slower transport of the resulting patterns across the tissue through morphogenesis.

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