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...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Wiley
2009-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2009/710353 |
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| _version_ | 1832560767085314048 |
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| author | Chunqing Wu Jing-an Cui |
| author_facet | Chunqing Wu Jing-an Cui |
| author_sort | Chunqing Wu |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-d6eb2057a573442c9691126972f2634d |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2009-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-d6eb2057a573442c9691126972f2634d2025-02-03T01:26:45ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2009-01-01200910.1155/2009/710353710353Global Dynamics of Discrete Competitive Models with Large Intrinsic Growth RatesChunqing Wu0Jing-an Cui1School of Mathematical Sciences, Nanjing Normal University, Nanjing 210097, ChinaSchool of Mathematical Sciences, Nanjing Normal University, Nanjing 210097, ChinaThe 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.http://dx.doi.org/10.1155/2009/710353 |
| spellingShingle | Chunqing Wu Jing-an Cui Global Dynamics of Discrete Competitive Models with Large Intrinsic Growth Rates Discrete Dynamics in Nature and Society |
| title | Global Dynamics of Discrete Competitive Models with Large Intrinsic Growth Rates |
| title_full | Global Dynamics of Discrete Competitive Models with Large Intrinsic Growth Rates |
| title_fullStr | Global Dynamics of Discrete Competitive Models with Large Intrinsic Growth Rates |
| title_full_unstemmed | Global Dynamics of Discrete Competitive Models with Large Intrinsic Growth Rates |
| title_short | Global Dynamics of Discrete Competitive Models with Large Intrinsic Growth Rates |
| title_sort | global dynamics of discrete competitive models with large intrinsic growth rates |
| url | http://dx.doi.org/10.1155/2009/710353 |
| work_keys_str_mv | AT chunqingwu globaldynamicsofdiscretecompetitivemodelswithlargeintrinsicgrowthrates AT jingancui globaldynamicsofdiscretecompetitivemodelswithlargeintrinsicgrowthrates |