On Predator-Prey Systems and Small-Gain Theorems
This paper deals with an almost global convergence result forLotka-Volterra systems with predator-prey interactions. These systems canbe written as (negative) feedback systems. The subsystems of the feedbackloop are monotone control systems, possessing particular input-outputproperties. We use a sm...
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| Format: | Article |
| Language: | English |
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AIMS Press
2004-10-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2005.2.25 |
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| _version_ | 1832590270047191040 |
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| author | Patrick D. Leenheer David Angeli Eduardo D. Sontag |
| author_facet | Patrick D. Leenheer David Angeli Eduardo D. Sontag |
| author_sort | Patrick D. Leenheer |
| collection | DOAJ |
| description | This paper deals with an almost global convergence result forLotka-Volterra systems with predator-prey interactions. These systems canbe written as (negative) feedback systems. The subsystems of the feedbackloop are monotone control systems, possessing particular input-outputproperties. We use a small-gain theorem, adapted to a context of systemswith multiple equilibrium points to obtain the desired almost globalconvergence result, which provides sufficient conditions to rule outoscillatory or more complicated behavior that is often observed inpredator-prey systems. |
| format | Article |
| id | doaj-art-92c806a637744e02bcdda15d2a072e06 |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2004-10-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-92c806a637744e02bcdda15d2a072e062025-01-24T01:47:55ZengAIMS PressMathematical Biosciences and Engineering1551-00182004-10-0121254210.3934/mbe.2005.2.25On Predator-Prey Systems and Small-Gain TheoremsPatrick D. Leenheer0David Angeli1Eduardo D. Sontag2Department of Mathematics, University of Florida, Gainesville, FL 32611-8105Dip. di Sistemi e Informatica, Universitá di Firenze, Via di S. Marta 3, 50139 FirenzeDepartment of Mathematics, Rutgers University, New Brunswick, NJ 08903This paper deals with an almost global convergence result forLotka-Volterra systems with predator-prey interactions. These systems canbe written as (negative) feedback systems. The subsystems of the feedbackloop are monotone control systems, possessing particular input-outputproperties. We use a small-gain theorem, adapted to a context of systemswith multiple equilibrium points to obtain the desired almost globalconvergence result, which provides sufficient conditions to rule outoscillatory or more complicated behavior that is often observed inpredator-prey systems.https://www.aimspress.com/article/doi/10.3934/mbe.2005.2.25monotone systemsfeedback systemslotka-volterra systems.almost global stability |
| spellingShingle | Patrick D. Leenheer David Angeli Eduardo D. Sontag On Predator-Prey Systems and Small-Gain Theorems Mathematical Biosciences and Engineering monotone systems feedback systems lotka-volterra systems. almost global stability |
| title | On Predator-Prey Systems and Small-Gain Theorems |
| title_full | On Predator-Prey Systems and Small-Gain Theorems |
| title_fullStr | On Predator-Prey Systems and Small-Gain Theorems |
| title_full_unstemmed | On Predator-Prey Systems and Small-Gain Theorems |
| title_short | On Predator-Prey Systems and Small-Gain Theorems |
| title_sort | on predator prey systems and small gain theorems |
| topic | monotone systems feedback systems lotka-volterra systems. almost global stability |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2005.2.25 |
| work_keys_str_mv | AT patrickdleenheer onpredatorpreysystemsandsmallgaintheorems AT davidangeli onpredatorpreysystemsandsmallgaintheorems AT eduardodsontag onpredatorpreysystemsandsmallgaintheorems |