title: Generating functionals and Gaussian approximations for interruptible 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 generalizes 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.
authors.affiliation: Theoretical Physics, School of Physics and Astronomy, The University of Manchester, Manchester M13 9PL, United Kingdom.|Department of Ecology and Evolutionary Biology, University of Michigan, Ann Arbor, Michigan 48109, USA.|Center for the Study of Complex Systems, University of Michigan, Ann Arbor, Michigan 48109, USA.
authors.forename: Tobias
authors.initials: T
authors.lastname: Brett
authors.affiliation: Theoretical Physics, School of Physics and Astronomy, The University of Manchester, Manchester M13 9PL, United Kingdom.
authors.forename: Tobias
authors.initials: T
authors.lastname: Galla
mesh_terms: D000818:Animals; D003141:Communicable Diseases / Q000401:mortality; D004198:Disease Susceptibility; D006801:Humans; D016014:Linear Models; D008962:Models, Theoretical; D016011:Normal Distribution; D011235:Predatory Behavior; D012098:Reproduction