The threshold of survival for systems in a fluctuating environment
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.
scientific article; zbMATH DE number 4108560