Information flow and information production in a population system.

Area of Science:

• * Population dynamics
• * Information theory
• * Stochastic processes

Background:

• * Quantifying information flow in evolving systems is crucial for understanding complex behaviors.
• * Existing models often lack a dynamic framework to capture information changes over time.
• * Population evolution, particularly logistic-like growth, presents unique challenges for information analysis.

Purpose of the Study:

• * To develop a quantitative approach for measuring information dynamics within a population.
• * To analyze the behavior of information entropy flux and production during system evolution.
• * To investigate the relationship between population growth phases and information entropy changes.

Main Methods:

• * Mapping system evolution to a birth and death type stochastic process.
• * Deriving a balance equation for information entropy.
• * Analyzing time-dependent properties and parameter dependencies of information entropy flux and production.

Main Results:

• * Identified and analyzed information entropy flux and production over time.
• * Demonstrated the existence of minimum information entropy production states under specific parameter values.
• * Observed transient intensification of uncertainty and information production at the logistic-like growth inflexion point.

Conclusions:

• * The developed stochastic process model effectively quantifies population information dynamics.
• * Minimum information entropy production is achievable, suggesting system optimization possibilities.
• * Population growth phases significantly impact information entropy, with inflexion points being critical stages.