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Interference: Path Lengths

Interference: Path Lengths

Consider two sources of sound, that may or may not be in phase, emitting waves at a single frequency, and consider the frequencies to be the same.
Two special sources may be considered when they are in phase. This can be easily achieved by feeding the two sources from the same source. An example would be synchronizing the two speakers by feeding them with the same source, such as the sound waves produced by a tuning fork. This setup ensures that the two sources have the same frequency and are...

Time and frequency -Domain Interpretation of PI Control

Time and frequency -Domain Interpretation of PI Control

Proportional-Integral (PI) controllers are essential in many control systems to improve stability and performance. They are commonly used in everyday devices like thermostats to enhance system damping and reduce steady-state error. When the zero in the controller's transfer function is optimally placed, the system benefits significantly in terms of stability and accuracy.
Acting as a low-pass filter, the PI controller slows the system's response and extends settling times. This requires careful...

Phase-lead and Phase-lag Controllers

Phase-lead and Phase-lag Controllers

Understanding the working function of different types of controllers can be illustrated with practical analogies, such as adjusting a stereo's volume equalizer. Cranking up the bass involves a phase-lead controller, which functions as a high-pass filter, while increasing the treble uses a phase-lag controller, which acts as a low-pass filter. PD controllers, similar to high-pass filters, enhance the system's response to high-frequency components. PI controllers, akin to low-pass filters, manage...

Time and frequency -Domain Interpretation of Phase-lead Control

Time and frequency -Domain Interpretation of Phase-lead Control

Phase-lead controllers are commonly used in various control systems to enhance response speed and stability. Adjusting the brightness on a television screen offers a practical example of phase-lead control. When contrast is enhanced, a phase-lead controller is employed. Mathematically, phase-lead control is identified when the first parameter is smaller than the second.
The design of phase-lead control involves the strategic placement of poles and zeros to balance steady-state error and system...

Time and frequency -Domain Interpretation of Phase-lag Control

Time and frequency -Domain Interpretation of Phase-lag Control

Phase-lag controllers are widely used in control systems to improve stability and reduce steady-state errors. A dimmer switch controlling the brightness of a light bulb serves as a practical example of phase-lag control, gradually adjusting the bulb's brightness. Mathematically, phase-lag control or low-pass filtering is represented when the factor 'a' is less than 1.
Phase-lag controllers do not place a pole at zero, but instead influence the steady-state error by amplifying any finite,...

Load-frequency control

Load-frequency control

Load-frequency control (LFC) is vital for maintaining power system stability, ensuring that frequency and power flows remain within acceptable limits during load changes. Turbine-governor control eliminates rotor accelerations and decelerations following load changes. However, a steady-state frequency error persists when the change in the turbine-governor reference setting is zero. In an interconnected power system, each area agrees to export or import a scheduled amount of power through...

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Related Experiment Video

Updated: Jul 8, 2026

Time-dependent Increase in the Network Response to the Stimulation of Neuronal Cell Cultures on Micro-electrode Arrays

Time-dependent Increase in the Network Response to the Stimulation of Neuronal Cell Cultures on Micro-electrode Arrays

Published on: May 29, 2017

Local network parameters can affect inter-network phase lags in central pattern generators.

S R Jones¹, N Kopell

¹Athinoula A. Martinos Center for Biomedical Imaging, Massachusetts General Hospital, Charlestown, MA 02129, USA. srjones@nmr.mgh.harvard.edu

Journal of Mathematical Biology

|October 1, 2005

Summary

This study examines how combined weak and strong coupling mechanisms in neural networks create stable phase lags. It reveals how local network parameters, like inhibition decay time, influence inter-network phase differences in central pattern generators.

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Area of Science:

Computational Neuroscience
Systems Neuroscience
Biophysics

Background:

Oscillators exhibit distinct coupling mechanisms (weak vs. strong) influencing phase lag stability.
Central pattern generators (CPGs) often integrate both weak and strong coupling features.
Understanding phase lag generation is crucial for CPG function.

Purpose of the Study:

To analyze phase lags in systems combining weakly coupled networks of strongly coupled oscillators.
To investigate the impact of local network parameters on inter-network phase lags.
To model the crayfish CPG for swimming.

Main Methods:

Application of geometrical singular perturbation theory.
Analysis of coupled relaxation oscillator networks.
Modeling of neural network dynamics.

Main Results:

Demonstrated how combined weak and strong coupling mechanisms produce stable phase lags.
Identified specific local network parameters, such as decay time of inhibition, that modulate inter-network phase lags.
Provided a theoretical framework applicable to biological CPGs.

Conclusions:

The interplay between local strong coupling and weak inter-network coupling dictates phase lag dynamics in CPGs.
Local network parameters offer a mechanism for fine-tuning inter-network phase relationships.
The findings offer insights into the control of rhythmic motor behaviors like swimming.