Beyond the adiabatic limit in systems with fast environments: A τ-leaping algorithm

Ernesto Berríos-Caro and Tobias Galla
Phys. Rev. E 104, 014122 – Published 19 July 2021

Abstract

We propose a τ-leaping simulation algorithm for stochastic systems subject to fast environmental changes. Similar to conventional τ-leaping the algorithm proceeds in discrete time steps, but as a principal addition it captures environmental noise beyond the adiabatic limit. The key idea is to treat the input rates for the τ-leaping as (clipped) Gaussian random variables with first and second moments constructed from the environmental process. In this way, each step of the algorithm retains environmental stochasticity to subleading order in the timescale separation between system and environment. We test the algorithm on several toy examples with discrete and continuous environmental states and find good performance in the regime of fast environmental dynamics. At the same time, the algorithm requires significantly less computing time than full simulations of the combined system and environment. In this context we also discuss several methods for the simulation of stochastic population dynamics in time-varying environments with continuous states.

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  • Received 21 November 2020
  • Revised 17 May 2021
  • Accepted 21 June 2021

DOI:https://doi.org/10.1103/PhysRevE.104.014122

©2021 American Physical Society

Physics Subject Headings (PhySH)

Statistical Physics & ThermodynamicsPhysics of Living Systems

Authors & Affiliations

Ernesto Berríos-Caro1,* and Tobias Galla1,2,†

  • 1Theoretical Physics, Department of Physics and Astronomy, School of Natural Sciences, Faculty of Science and Engineering, The University of Manchester, Manchester M13 9PL, United Kingdom
  • 2Instituto de Física Interdisciplinar y Sistemas Complejos, IFISC (CSIC-UIB), Campus Universitat Illes Balears, E-07122 Palma de Mallorca, Spain

  • *ernesto.berrios@postgrad.manchester.ac.uk
  • tobias.galla@ifisc.uib-csic.es

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Issue

Vol. 104, Iss. 1 — July 2021

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