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Related Concept Videos

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:
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...
Skewness01:06

Skewness

The measures of central tendency calculated from a data set may not reveal much about its intrinsic distribution. If a plot is made of the data set’s values, the mean and the median may not only differ, but also the plot may have more values on one side of the central tendencies. Such a data set is said to be skewed towards that side.
The longer the tail of the plot on one side, the more skewed it is. The skewness of a data set’s values suggests that the measures of central tendency are...
Types of Skewness01:09

Types of Skewness

If the frequency distribution of a data set is more inclined towards smaller or larger values, the distribution is said to be skewed. If data values are skewed to the right, then the distribution is called positively skewed. Conversely, if the plot is skewed to the left, the distribution is called negatively skewed.
For instance, in the middle of a pandemic, the geographical distribution of vaccine coverage may be positively skewed towards populations in the global north countries. However,...
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.
Factors Affecting the Risk of Infection01:26

Factors Affecting the Risk of Infection

The hosts' susceptibility to infection depends on several factors. The integrity of the skin and mucous membranes helps protect the body against microbial attacks. When the skin is altered, the chance of infection, limb loss, and even death increases.
The integrity and count of the white blood cells help the body resist pathogens and fight infection. When impaired, it reduces the body's resistance to pathogens. The acidic pH levels of the gastrointestinal, genitourinary tracts, and skin create...

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Related Experiment Video

Updated: Jun 22, 2026

Peering into the Dynamics of Social Interactions: Measuring Play Fighting in Rats
15:01

Peering into the Dynamics of Social Interactions: Measuring Play Fighting in Rats

Published on: January 18, 2013

Skewed attacks, stability, and host suppression.

Abhyudai Singh1, William W Murdoch, Roger M Nisbet

  • 1Department of Ecology, Evolution and Marine Biology, University of California, Santa Barbara, California 93106, USA. a2singh@ucsd.edu

Ecology
|July 3, 2009
PubMed
Summary
This summary is machine-generated.

Parasitoid-host population stability depends critically on how risk of parasitism is distributed among hosts. A skewed distribution with zero modal risk is essential for stabilizing host-parasitoid dynamics across all host reproduction rates.

Related Experiment Videos

Last Updated: Jun 22, 2026

Peering into the Dynamics of Social Interactions: Measuring Play Fighting in Rats
15:01

Peering into the Dynamics of Social Interactions: Measuring Play Fighting in Rats

Published on: January 18, 2013

Area of Science:

  • Ecology
  • Population Dynamics
  • Mathematical Biology

Background:

  • The Nicholson-Bailey model describes host-parasitoid interactions.
  • Population stability can be achieved through variation in parasitism risk among hosts.

Purpose of the Study:

  • To investigate the crucial role of the distribution shape of parasitism risk in stabilizing host-parasitoid dynamics.
  • To develop a general stability criterion for host-parasitoid equilibria.

Main Methods:

  • Analysis of the Nicholson-Bailey framework.
  • Mathematical modeling of host-parasitoid population dynamics.
  • Investigation of risk distribution shapes and their impact on stability.

Main Results:

  • The shape of the risk distribution is critical for stability.
  • Stability across all host reproduction rates (R) requires a distribution skewed towards zero modal risk.
  • Distributions with a non-zero mode, even with high variability, may not stabilize the equilibrium for certain R values.
  • A new, general stability criterion is established: equilibrium is stable if adult host density increases with R.

Conclusions:

  • Skewed parasitism risk, particularly with a modal risk of zero, is key to stabilizing host-parasitoid interactions.
  • This type of skewed risk reduces parasitoid efficiency, limiting host suppression.
  • Field measures can be identified to link parasitism risk skew to population stability.