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Related Concept Videos

BIBO stability of continuous and discrete -time systems01:24

BIBO stability of continuous and discrete -time systems

System stability is a fundamental concept in signal processing, often assessed using convolution. For a system to be considered bounded-input bounded-output (BIBO) stable, any bounded input signal must produce a bounded output signal. A bounded input signal is one where the modulus does not exceed a certain constant at any point in time.
To determine the BIBO stability, the convolution integral is utilized when a bounded continuous-time input is applied to a Linear Time-Invariant (LTI) system.
Multimachine Stability01:25

Multimachine Stability

Multimachine stability analysis is crucial for understanding the dynamics and stability of power systems with multiple synchronous machines. The objective is to solve the swing equations for a network of M machines connected to an N-bus power system.
In analyzing the system, the nodal equations represent the relationship between bus voltages, machine voltages, and machine currents. The nodal equation is given by:
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...
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-Domain Interpretation of PD Control01:07

Time-Domain Interpretation of PD Control

Proportional-Derivative (PD) control is a widely used control method in various engineering systems to enhance stability and performance. In a system with only proportional control, common issues include high maximum overshoot and oscillation, observed in both the error signal and its rate of change. This behavior can be divided into three distinct phases: initial overshoot, subsequent undershoot, and gradual stabilization.
Consider the example of control of motor torque. Initially, a positive...
Transmission-Line Differential Equations01:26

Transmission-Line Differential Equations

Transmission lines are essential components of electrical power systems. They are characterized by the distributed nature of resistance (R), inductance (L), and capacitance (C) per unit length. To analyze these lines, differential equations are employed to model the variations in voltage and current along the line.
Line Section Model
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Related Experiment Video

Updated: Jul 4, 2026

Inherent Dynamics Visualizer, an Interactive Application for Evaluating and Visualizing Outputs from a Gene Regulatory Network Inference Pipeline
10:44

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Published on: December 7, 2021

Can distributed delays perfectly stabilize dynamical networks?

Takahiro Omi1, Shigeru Shinomoto

  • 1Department of Physics, Kyoto University, Sakyo-ku, Kyoto 606-8502, Japan. omi@ton.scphys.kyoto-u.ac.jp

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|June 4, 2008
PubMed
Summary

Signal transmission delays can destabilize neural networks. However, increasing delay dispersion, especially beyond exponential distribution, enhances network stability, preventing oscillations.

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Area of Science:

  • Dynamical systems
  • Computational neuroscience
  • Network theory

Background:

  • Signal transmission delays are inherent in neural networks.
  • These delays can lead to network instability and oscillations.
  • Delay dispersion, the variation in delay times, also influences network dynamics.

Purpose of the Study:

  • To analyze the impact of distributed signal delays on neural network dynamics.
  • To investigate how delay dispersion affects network stability.
  • To explore phenomena like reentrant stability in neural systems.

Main Methods:

  • Analysis of an integrodifferential equation modeling neural network dynamics.
  • Mathematical modeling of collective dynamics with distributed signal delays.
  • Comparison of Gamma and exponential delay distributions.

Main Results:

  • Gamma distributed delays, less dispersed than exponential, can cause reentrant phenomena where stability is lost and then recovered.
  • Highly dispersed delays, exceeding exponential distribution, lead to persistent network stabilization.
  • Delay dispersion acts as a stabilizing factor against oscillations.

Conclusions:

  • The dispersion of signal transmission delays is a critical factor in neural network stability.
  • Tailoring delay distribution can control network dynamics and prevent destabilizing oscillations.
  • Understanding delay dispersion is key for designing robust and stable artificial neural networks.