Global Dynamics of Discrete Competitive Models with Large Intrinsic Growth Rates
The global dynamics of discrete competitive model of Lotka-Volterra type with two species is considered. Earlier works have shown that the unique positive equilibrium is globally attractive under the assumption that the intrinsic growth rates of the two competitive species are less than 1+ln 2, and...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Hindawi Limited
2009-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2009/710353 |
| Summary: | The global dynamics of discrete competitive model of Lotka-Volterra type with two species
is considered. Earlier works have shown that the unique positive equilibrium is globally attractive under
the assumption that the intrinsic growth rates of the two competitive species are less than 1+ln 2, and
further the unique positive equilibrium is globally asymptotically stable under the stronger condition
that the intrinsic growth rates of the two competitive species are less than or equal to 1. We prove
that the system can also be globally asymptotically stable when the intrinsic growth rates of the two
competitive species are greater than 1 and globally attractive when the intrinsic growth rates of the two competitive species are greater than 1 + ln 2. |
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| ISSN: | 1026-0226 1607-887X |