Abstract
The dynamics of a differential functional equation system representing an allelopathic competition is analyzed. The delayed allelochemical production process is represented by means of a distributed delay term in a linear quorum-sensing model. Sufficient conditions for local asymptotic stability properties of biologically meaningful steady-state solutions are given in terms of the parameters of the system. A global asymptotic stability result is also proved by constructing a suitable Lyapunov functional. Some simulations confirm the analytical results.
| Original language | English |
|---|---|
| Pages (from-to) | 37-50 |
| Number of pages | 14 |
| Journal | Mathematical Biosciences and Engineering |
| Volume | 3 |
| Issue number | 1 |
| Early online date | 1 Nov 2005 |
| DOIs | |
| Publication status | Published - 1 Jan 2006 |
Keywords
- Allelopathy
- Chemostat models
- Distributed delay
- Global stability
- Quorum sensing