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The threshold of survival for systems in a fluctuating environment. (English) Zbl 0676.92010
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.
Reviewer: Bingxi Li

MSC:
 92D40 Ecology 92D25 Population dynamics (general)
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References:
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