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Related Concept Videos

Network Function of a Circuit01:25

Network Function of a Circuit

Frequency response analysis in electrical circuits provides vital insights into a circuit's behavior as the frequency of the input signal changes. The transfer function, a mathematical tool, is instrumental in understanding this behavior. It defines the relationship between phasor output and input and comes in four types: voltage gain, current gain, transfer impedance, and transfer admittance. The critical components of the transfer function are the poles and zeros.
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:
Sequence Networks of Rotating Machines01:24

Sequence Networks of Rotating Machines

A Y-connected synchronous generator, grounded through a neutral impedance, is designed to produce balanced internal phase voltages with only positive-sequence components. The generator's sequence networks include a source voltage that is exclusively in the positive-sequence network. The sequence components of line-to-ground voltages at the generator terminals illustrate this configuration.
Zero-sequence current induces a voltage drop across the generator's neutral impedance and other...
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...
Equivalent Resistance01:16

Equivalent Resistance

In circuit analysis, situations often arise where resistors are neither in series nor parallel configurations. To tackle such scenarios, three-terminal equivalent networks like the wye (Y) (Figure 1 (a)) or tee (T) and delta (Δ) (Figure 1 (b)) or pi (π) networks come into play. These networks offer versatile solutions and are frequently encountered in various applications, including three-phase electrical systems, electrical filters, and matching networks.

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Related Experiment Video

Updated: Jun 14, 2026

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

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

Published on: December 7, 2021

Boolean networks with reliable dynamics.

Tiago P Peixoto1, Barbara Drossel

  • 1Institut für Festkörperphysik, TU Darmstadt, Hochschulstrasse 6, 64289 Darmstadt, Germany. tiago@fkp.tu-darmstadt.de

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|April 7, 2010
PubMed
Summary
This summary is machine-generated.

Boolean networks with reliable trajectories exhibit higher clustering and a prevalence of canalyzing functions. As network size increases, fixed points become more dominant, indicating a shift towards a frozen state.

Related Experiment Videos

Last Updated: Jun 14, 2026

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

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

Published on: December 7, 2021

Area of Science:

  • Computational Biology
  • Network Science
  • Systems Biology

Background:

  • Boolean networks are widely used to model complex biological systems.
  • Understanding network dynamics and state space properties is crucial for biological insights.
  • Reliable trajectories offer a unique perspective on network behavior independent of update order.

Purpose of the Study:

  • To investigate the structural and dynamical properties of Boolean networks following reliable trajectories.
  • To characterize the topology, update functions, and state space of these networks.
  • To compare these properties with random networks and gene regulation networks.

Main Methods:

  • Numerical exploration of Boolean networks constructed with minimal links and simple update functions.
  • Analysis of network topology, including clustering coefficient and three-node motifs.
  • Classification and probability assessment of update functions.
  • Study of state space structure and fixed point dominance with increasing system size.

Main Results:

  • Boolean networks with reliable trajectories show a higher clustering coefficient than random networks.
  • The distribution of three-node motifs resembles that of gene regulation networks.
  • A specific subset of update functions, predominantly canalyzing functions, occurs frequently.
  • Increasing system size leads to increased dominance of fixed points, approaching a frozen phase.

Conclusions:

  • Boolean networks supporting reliable trajectories possess distinct topological and functional characteristics.
  • The prevalence of canalyzing functions suggests efficient information processing or stability mechanisms.
  • The observed shift towards fixed points indicates a tendency towards stable states in larger systems.