×

zbMATH — the first resource for mathematics

Effect of randomly fluctuating environment on autotroph-herbivore model system. (English) Zbl 1077.34063
The authors consider a noninteractive type of autotroph-herbivore model system in which the removal rate of autotroph biomass has been taken as a Holling type -III function and they derive a local asymptotic stability condition and the existence of small amplitude periodic solution within a deterministic environment. The deterministic model is randomized by introducing additive Gaussian white noise leading to a system of ItĂ´ type of stochastic differential equation. Stochastic stability criteria of the model system under the influence of random environmental fluctuation are obtained through the convergence conditions of second-order moments.

MSC:
34F05 Ordinary differential equations and systems with randomness
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
34C60 Qualitative investigation and simulation of ordinary differential equation models
92B05 General biology and biomathematics
34C23 Bifurcation theory for ordinary differential equations
34D20 Stability of solutions to ordinary differential equations
PDF BibTeX XML Cite
Full Text: DOI EuDML