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Pole and System Stability

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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.
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Microtubule Instability

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Related Experiment Video

Updated: May 28, 2026

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

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

Published on: December 7, 2021

Prosperity is associated with instability in dynamical networks.

Matteo Cavaliere¹, Sean Sedwards, Corina E Tarnita

¹The Microsoft Research-University of Trento Centre for Computational and Systems Biology, Povo (Trento) 38123, Italy.

Journal of Theoretical Biology

|October 11, 2011

Summary

This summary is machine-generated.

Cooperators build prosperous, connected networks, while defectors cause fragmentation. This dynamic of cooperation and defection drives cycles of network formation and decline in social and biological systems.

Related Experiment Videos

Last Updated: May 28, 2026

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

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:

Network Science
Game Theory
Sociology
Ecology

Background:

Social, biological, and economic networks exhibit dynamic changes including fragmentation and re-formation.
These network dynamics are often attributed to external factors or perturbations.

Purpose of the Study:

To investigate the role of simple imitation and internal conflicts between cooperators and defectors in driving network dynamics.
To model how cooperation and defection influence network structure, prosperity, and stability.

Main Methods:

Utilized a game-theoretic model of dynamic network formation.
Simulated newcomer imitation of successful individuals' strategies and social networks.

Main Results:

Cooperators foster well-connected, prosperous networks.
Defectors invade and fragment networks, leading to loss of prosperity.
Fragmented networks can be re-established by cooperators, creating cycles of formation and fragmentation.

Conclusions:

Internal dynamics of cooperation and defection, not just external perturbations, drive network evolution.
Cooperation leads to prosperity but also instability in dynamic networks.
Frequent network formation and fragmentation favor cooperation's prosperity.