Necessary and sufficient average growth in a Lotka-Volterra system. (English) Zbl 0934.34037
The authors consider a Lotka-Volterra system in which the growth rates may fluctuate about long-term averages. An extension of the “principle of competitive exclusion” is given. “Almost necessary and sufficient” conditions for one species to be driven to extinction are derived and proved. Some results for the linear system and the linearized stability are obtained.
Reviewer: Jihong Dou (Xian)
MSC:
| 34C60 | Qualitative investigation and simulation of ordinary differential equation models |
| 34C11 | Growth and boundedness of solutions to ordinary differential equations |
| 34D05 | Asymptotic properties of solutions to ordinary differential equations |
| 34F05 | Ordinary differential equations and systems with randomness |
| 34C29 | Averaging method for ordinary differential equations |
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