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Related Concept Videos

Time and frequency -Domain Interpretation of Phase-lag Control01:21

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,...
Linear time-invariant Systems01:23

Linear time-invariant Systems

A system is linear if it displays the characteristics of homogeneity and additivity, together termed the superposition property. This principle is fundamental in all linear systems. Linear time-invariant (LTI) systems include systems with linear elements and constant parameters.
The input-output behavior of an LTI system can be fully defined by its response to an impulsive excitation at its input. Once this impulse response is known, the system's reaction to any other input can be calculated...
Time and frequency -Domain Interpretation of Phase-lead Control01:24

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...
Propagation of Uncertainty from Random Error00:59

Propagation of Uncertainty from Random Error

An experiment often consists of more than a single step. In this case, measurements at each step give rise to uncertainty. Because the measurements occur in successive steps, the uncertainty in one step necessarily contributes to that in the subsequent step. As we perform statistical analysis on these types of experiments, we must learn to account for the propagation of uncertainty from one step to the next. The propagation of uncertainty depends on the type of arithmetic operation performed on...
Distributed Loads: Problem Solving01:21

Distributed Loads: Problem Solving

Beams are structural elements commonly employed in engineering applications requiring different load-carrying capacities. The first step in analyzing a beam under a distributed load is to simplify the problem by dividing the load into smaller regions, which allows one to consider each region separately and calculate the magnitude of the equivalent resultant load acting on each portion of the beam. The magnitude of the equivalent resultant load for each region can be determined by calculating...
Propagation of Uncertainty from Systematic Error01:10

Propagation of Uncertainty from Systematic Error

The atomic mass of an element varies due to the relative ratio of its isotopes. A sample's relative proportion of oxygen isotopes influences its average atomic mass. For instance, if we were to measure the atomic mass of oxygen from a sample, the mass would be a weighted average of the isotopic masses of oxygen in that sample. Since a single sample is not likely to perfectly reflect the true atomic mass of oxygen for all the molecules of oxygen on Earth, the mass we obtain from this particular...

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Related Experiment Video

Updated: May 16, 2026

Assessing the Multiple Dimensions of Engagement to Characterize Learning: A Neurophysiological Perspective
13:57

Assessing the Multiple Dimensions of Engagement to Characterize Learning: A Neurophysiological Perspective

Published on: July 1, 2015

Network coordination and synchronization in a noisy environment with time delays.

D Hunt1, B K Szymanski, G Korniss

  • 1Department of Physics, Applied Physics, and Astronomy, Rensselaer Polytechnic Institute, 110 8th Street, Troy, New York 12180-3590, USA.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|December 11, 2012
PubMed
Summary

Time delays in complex networks impact stochastic synchronization. This study analyzes transmission and local delays, revealing how they affect synchronizability thresholds and network behavior for various coupling schemes.

Related Experiment Videos

Last Updated: May 16, 2026

Assessing the Multiple Dimensions of Engagement to Characterize Learning: A Neurophysiological Perspective
13:57

Assessing the Multiple Dimensions of Engagement to Characterize Learning: A Neurophysiological Perspective

Published on: July 1, 2015

Area of Science:

  • Complex networks
  • Stochastic systems
  • Nonlinear dynamics

Background:

  • Synchronization is crucial in complex systems.
  • Time delays can significantly alter system dynamics.
  • Understanding delay effects is key for network stability.

Purpose of the Study:

  • Investigate the impact of transmission and local time delays on stochastic synchronization in complex networks.
  • Determine how different delay schemes influence synchronizability thresholds and network behavior.
  • Analyze the scaling of synchronization landscape width under various network coupling conditions.

Main Methods:

  • Analytical investigation of fluctuations for different delay schemes.
  • Derivation of synchronizability thresholds and scaling behavior.
  • Numerical computations for complex network scenarios where analytical solutions are unavailable.

Main Results:

  • Established methods to determine synchronizability thresholds and scaling behavior for networks with time delays.
  • Identified the influence of transmission and local delays on synchronization properties.
  • Characterized network behavior for arbitrary and specific weighted networks.

Conclusions:

  • Time delays introduce critical factors affecting stochastic synchronization in complex networks.
  • Findings offer insights into network coupling strategies and potential trade-offs.
  • The study provides a framework for analyzing delay-induced phenomena in networked systems.