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Related Concept Videos

Pole and System Stability01:24

Pole and System Stability

The transfer function is a fundamental concept representing the ratio of two polynomials. The numerator and denominator encapsulate the system's dynamics. The zeros and poles of this transfer function are critical in determining the system's behavior and stability.
Simple poles are unique roots of the denominator polynomial. Each simple pole corresponds to a distinct solution to the system's characteristic equation, typically resulting in exponential decay terms in the system's response.
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.
Stability01:28

Stability

The time response of a linear time-invariant (LTI) system can be divided into transient and steady-state responses. The transient response represents the system's initial reaction to a change in input and diminishes to zero over time. In contrast, the steady-state response is the behavior that persists after the transient effects have faded.
The stability of an LTI system is determined by the roots of its characteristic equation, known as poles. A system is stable if it produces a bounded...
One-Degree-of-Freedom System01:24

One-Degree-of-Freedom System

In mechanical engineering, one-degree-of-freedom systems form the basis of a wide range of electrical and mechanical components. Using these models, engineers can predict the behavior of various parts in a larger system, which gives them insight into how different forces interact with each other.
A one-degree-of-freedom system is defined by an independent variable that determines its state and behavior. One example of a one-degree-of-freedom system is a simple harmonic oscillator, such as a...
Routh-Hurwitz Criterion II01:19

Routh-Hurwitz Criterion II

In the application of the Routh-Hurwitz criterion, two specific scenarios can arise that complicate stability analysis.
The first scenario occurs when a singular zero appears in the first column of the Routh table. This situation creates a division by zero issues. To resolve this, a small positive or negative number, denoted as epsilon (โˆˆ), is substituted for the zero. The stability analysis proceeds by assuming a sign for โˆˆ. If โˆˆ is positive, any sign change in the first column of the Routh...
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:

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Updated: May 14, 2026

The Use of Chemostats in Microbial Systems Biology
13:19

The Use of Chemostats in Microbial Systems Biology

Published on: October 14, 2013

Bistability in one equation or fewer.

Graham A Anderson1, Xuedong Liu, James E Ferrell

  • 1Chemical and Systems Biology, Stanford University Medical Center, Stanford, CA, USA.

Methods in Molecular Biology (Clifton, N.J.)
|January 31, 2013
PubMed
Summary
This summary is machine-generated.

Graphical methods can reveal emergent behaviors in biological networks with feedback loops, like bistability and irreversibility. This approach offers an intuitive alternative to complex mathematical analysis for experimental data.

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Area of Science:

  • Systems biology
  • Biophysics
  • Computational biology

Background:

  • Gene and protein networks exhibit emergent behaviors not predictable from individual components.
  • Feedback loops in biological networks necessitate specialized analytical tools for understanding system dynamics.
  • Traditional analysis often relies on complex mathematical models like ordinary differential equations.

Purpose of the Study:

  • To present purely graphical methods for analyzing biological network behaviors.
  • To determine the plausibility of bistability and irreversibility in experimental data using graphical tools.
  • To provide an intuitive approach for understanding emergent behaviors in networks with feedback loops.

Main Methods:

  • Utilizing graphical methods instead of ordinary differential equations for network analysis.
  • Applying iterative stability analysis, a graphical technique, for stability determination in two dimensions.
  • Using the Xenopus laevis oocyte maturation network as a case study.

Main Results:

  • Demonstrated the application of graphical methods to assess network behaviors.
  • Successfully employed iterative stability analysis to evaluate stability in a biological network.
  • Provided a visualizable framework for understanding complex network dynamics.

Conclusions:

  • Graphical methods offer a powerful and intuitive alternative for analyzing biological networks.
  • Iterative stability analysis is effective for determining network behaviors like bistability and irreversibility from experimental data.
  • This approach simplifies the study of emergent properties in complex biological systems.