Generating functionals and Gaussian approximations for interruptible delay reactions

TL;DR

This paper develops a generating functional framework for non-Markovian systems with delay reactions that can be interrupted, extending previous models, and derives Gaussian approximations to analyze delay effects on stochastic predator-prey dynamics.

Contribution

It introduces a generalized path-integral approach for delay reactions that can be terminated, providing a new analytical tool for non-Markovian stochastic systems.

Findings

Gaussian approximations valid for large populations

Delay impacts noise-induced predator-prey cycles

Extended theory includes interrupted delay reactions

Abstract

We develop a generating functional description of the dynamics of non-Markovian individual-based systems, in which delay reactions can be terminated before completion. This generalises previous work in which a path-integral approach was applied to dynamics in which delay reactions complete with certainty. We construct a more widely applicable theory, and from it we derive Gaussian approximations of the dynamics, valid in the limit of large, but finite population sizes. As an application of our theory we study predator-prey models with delay dynamics due to gestation or lag periods to reach the reproductive age. In particular we focus on the effects of delay on noise-induced cycles.