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Global Dynamics of a Time-Delayed Microorganism Flocculation Model with Saturated Functional Responses.
- Source :
-
Journal of Dynamics & Differential Equations . Sep2018, Vol. 30 Issue 3, p1247-1271. 25p. - Publication Year :
- 2018
-
Abstract
- In this paper, a time-delayed model of microorganism flocculation with saturated functional responses is presented. We first analyse the local dynamics of this model with bifurcations in parameter fields, and then prove the collection of microorganisms is sustainable as well as obtain an explicit eventual lower bound of microorganism concentration when threshold parameter R0>1<inline-graphic></inline-graphic>. This model has a backward bifurcation if w<R0<1<inline-graphic></inline-graphic> under an additional condition, which implies that the microorganism-free equilibrium coexists with a microorganism equilibrium. In these cases, we establish some sufficient conditions for the global stability by using a variant of the Lyapunov-LaSalle theorem. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 10407294
- Volume :
- 30
- Issue :
- 3
- Database :
- Academic Search Index
- Journal :
- Journal of Dynamics & Differential Equations
- Publication Type :
- Academic Journal
- Accession number :
- 131207120
- Full Text :
- https://doi.org/10.1007/s10884-017-9605-3