The threshold of survival for systems in a fluctuating environment
type: Item
instance of: scholarly article
title: The threshold of survival for systems in a fluctuating environment
zbMATH Open document ID: 0676.92010
DOI: 10.1007/BF02460110
author: Zhien Ma
author: Thomas G. Hallam
author: Baojun Song
published in: Bulletin of Mathematical Biology
publication date: 1989-01-01T00:00:00Z
review text: Consider the following systems in a fluctuating environment: \[ (1)\quad dx/dt=(x/g(x))[r_ 0-r_ 1c_ T(t)-xf(x)],\quad t\in {\mathbb{R}}^ 1_+; \] \[ (2)\quad dx/dt=xF(r(t),x),\quad x\in {\mathbb{R}}^ 1_+\quad (Kolmogorov\quad model); \] \[ (3)\quad da/dt=f(t)-\beta ax,\quad dx/dt=x[r_ 0-r_ 1c_ T(t)-kxa^{-1}];\quad (Leslie\quad resource- consumer\quad model); \] \[ (4)\quad da/dt=f(t)-\omega x[1-\exp (-\eta a/x)],\quad dx/dt=x[r_ 0-r_ 1c_ T(t)-\gamma \omega \exp (-\eta a/x)],\quad (Gallopin\quad resource-consumer\quad model). \] The authors demonstrated the existence of a survival threshold for situations where demographic parameters are fluctuating, generally, in a nonperiodic manner. In general, the survival threshold is determined by a relationship between mean stress measure in organisms, the ratio of the population intrinsic growth rate and stress response rate. Five theorems are proved.
Mathematics Subject Classification ID: 92D40
Mathematics Subject Classification ID: 92D25
zbMATH DE Number: 4108560
zbMATH Keywords: fluctuating environment
zbMATH Keywords: Kolmogorov model
zbMATH Keywords: Leslie resource-consumer model
zbMATH Keywords: Gallopin resource-consumer model
zbMATH Keywords: survival threshold
zbMATH Keywords: intrinsic growth rate
zbMATH Keywords: stress response rate
Wikidata QID: Q69626516
reviewed by: Li Bingxi
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4108560