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Generating functionals and Gaussian approximations for interruptible delay reactions.

Tobias Brett1,2,3, Tobias Galla1

  • 1Theoretical Physics, School of Physics and Astronomy, The University of Manchester, Manchester M13 9PL, United Kingdom.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|November 14, 2015
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Summary
This summary is machine-generated.

We present a new theory for non-Markovian systems with incomplete delay reactions, applicable to large populations. This framework helps understand predator-prey dynamics and noise-induced cycles.

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Area of Science:

  • Mathematical modeling
  • Theoretical ecology
  • Statistical physics

Background:

  • Previous work focused on delay reactions completing with certainty.
  • A need exists for theories accommodating incomplete delay reactions in complex systems.

Purpose of the Study:

  • To develop a generalized generating functional description for non-Markovian individual-based systems.
  • To extend path-integral approaches to systems with terminable delay reactions.
  • To derive Gaussian approximations for large, finite population dynamics.

Main Methods:

  • Development of a generating functional description.
  • Application of path-integral methods.
  • Derivation of Gaussian approximations.
  • Analysis of predator-prey models with gestation or reproductive lag periods.

Main Results:

  • A more widely applicable theory for non-Markovian dynamics with incomplete delays.
  • Gaussian approximations valid for large, finite populations.
  • Insights into the effects of delay on noise-induced cycles in predator-prey models.

Conclusions:

  • The developed theory provides a robust framework for analyzing complex biological systems with delays.
  • The findings offer a deeper understanding of ecological dynamics, particularly predator-prey interactions influenced by noise and time lags.