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Sealable Femtoliter Chamber Arrays for Cell-free Biology
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Intrinsic noise and discrete-time processes.

Joseph D Challenger1, Duccio Fanelli, Alan J McKane

  • 1Dipartimento di Fisica e Astronomia, Università degli Studi di Firenze and INFN, via Sansone 1, IT 50019 Sesto Fiorentino, Italy.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|November 16, 2013
PubMed
Summary
This summary is machine-generated.

This study introduces a Markov chain model for population dynamics, capturing internal stochastic fluctuations. The model accurately describes systems, including the logistic map, in finite and infinite populations.

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Area of Science:

  • Mathematical modeling
  • Theoretical population dynamics
  • Stochastic processes

Background:

  • Traditional population models often assume deterministic dynamics or external noise.
  • Understanding internal stochasticity is crucial for realistic population simulations.
  • One-dimensional maps are fundamental tools in chaos theory and population dynamics.

Purpose of the Study:

  • To develop a general formalism for Markov chain models of one-dimensional maps.
  • To incorporate internal stochastic fluctuations within the model.
  • To provide a method for analyzing population dynamics in both finite and infinite populations.

Main Methods:

  • Constructing a Markov chain model that converges to a one-dimensional map.
  • Developing an approximate Gaussian scheme for stochastic fluctuations in finite populations.
  • Deriving a stochastic difference equation from the Markov chain approximation.

Main Results:

  • The developed formalism successfully models systems with internal stochasticity.
  • The approximate Gaussian scheme accurately describes fluctuations in the nonchaotic regime.
  • The logistic map was used as a case study, demonstrating the scheme's applicability.

Conclusions:

  • The formalism provides a robust framework for modeling population dynamics with internal stochasticity.
  • The stochastic difference equation offers a practical approach to capture complex dynamics.
  • This work advances the understanding of stochastic effects in theoretical population models.