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Structural stability of nonlinear population dynamics

Cenci, Simone; Saavedra, Serguei; (2018) Structural stability of nonlinear population dynamics. Physical Review E , 97 (1) , Article 012401. 10.1103/PhysRevE.97.012401. Green open access

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Abstract

In population dynamics, the concept of structural stability has been used to quantify the tolerance of a system to environmental perturbations. Yet, measuring the structural stability of nonlinear dynamical systems remains a challenging task. Focusing on the classic Lotka-Volterra dynamics, because of the linearity of the functional response, it has been possible to measure the conditions compatible with a structurally stable system. However, the functional response of biological communities is not always well approximated by deterministic linear functions. Thus, it is unclear the extent to which this linear approach can be generalized to other population dynamics models. Here, we show that the same approach used to investigate the classic Lotka-Volterra dynamics, which is called the structural approach, can be applied to a much larger class of nonlinear models. This class covers a large number of nonlinear functional responses that have been intensively investigated both theoretically and experimentally. We also investigate the applicability of the structural approach to stochastic dynamical systems and we provide a measure of structural stability for finite populations. Overall, we show that the structural approach can provide reliable and tractable information about the qualitative behavior of many nonlinear dynamical systems.

Type: Article
Title: Structural stability of nonlinear population dynamics
Location: United States
Open access status: An open access version is available from UCL Discovery
DOI: 10.1103/PhysRevE.97.012401
Publisher version: http://dx.doi.org/10.1103/physreve.97.012401
Language: English
Additional information: This version is the version of record. For information on re-use, please refer to the publisher’s terms and conditions.
Keywords: Science & Technology, Physical Sciences, Physics, Fluids & Plasmas, Physics, Mathematical, Physics, REORGANIZATION, NETWORKS, MODELS, NOISE
UCL classification: UCL
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of the Built Environment
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of the Built Environment > Bartlett School Env, Energy and Resources
URI: https://discovery-pp.ucl.ac.uk/id/eprint/10196473
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