Alternative models for cyclic lemming dynamics
Many natural population growths and interactions are affected byseasonal changes, suggesting that these natural population dynamicsshould be modeled by nonautonomous differential equations instead ofautonomous differential equations. Through a series of carefullyderived models of the well documented...
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AIMS Press
2006-10-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2007.4.85 |
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| author | Hao Wang Yang Kuang |
| author_facet | Hao Wang Yang Kuang |
| author_sort | Hao Wang |
| collection | DOAJ |
| description | Many natural population growths and interactions are affected byseasonal changes, suggesting that these natural population dynamicsshould be modeled by nonautonomous differential equations instead ofautonomous differential equations. Through a series of carefullyderived models of the well documented high-amplitude, large-periodfluctuations of lemming populations, we argue that whenappropriately formulated, autonomous differential equations maycapture much of the desirable rich dynamics, such as the existenceof a periodic solution with period and amplitude close to that ofapproximately periodic solutions produced by the more natural butmathematically daunting nonautonomous models. We start this seriesof models from the Barrow model, a well formulated model for thedynamics of food-lemming interaction at Point Barrow (Alaska, USA)with sufficient experimental data. Our work suggests that anautonomous system can indeed be a good approximation to themoss-lemming dynamics at Point Barrow. This, together with ourbifurcation analysis, indicates that neither seasonal factors(expressed by time-dependent moss growth rate and lemming death ratein the Barrow model) nor the moss growth rate and lemming death rateare the main culprits of the observed multi-year lemming cycles. Wesuspect that the main culprits may include high lemming predationrate, high lemming birth rate, and low lemming self-limitation rate. |
| format | Article |
| id | doaj-art-d4b99b03ba2c47d8a995ab96d768998a |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2006-10-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-d4b99b03ba2c47d8a995ab96d768998a2025-01-24T01:52:54ZengAIMS PressMathematical Biosciences and Engineering1551-00182006-10-0141859910.3934/mbe.2007.4.85Alternative models for cyclic lemming dynamicsHao Wang0Yang Kuang1Department of Mathematics and Statistics, Arizona State University, Tempe, AZ 85287Department of Mathematics and Statistics, Arizona State University, Tempe, AZ 85287Many natural population growths and interactions are affected byseasonal changes, suggesting that these natural population dynamicsshould be modeled by nonautonomous differential equations instead ofautonomous differential equations. Through a series of carefullyderived models of the well documented high-amplitude, large-periodfluctuations of lemming populations, we argue that whenappropriately formulated, autonomous differential equations maycapture much of the desirable rich dynamics, such as the existenceof a periodic solution with period and amplitude close to that ofapproximately periodic solutions produced by the more natural butmathematically daunting nonautonomous models. We start this seriesof models from the Barrow model, a well formulated model for thedynamics of food-lemming interaction at Point Barrow (Alaska, USA)with sufficient experimental data. Our work suggests that anautonomous system can indeed be a good approximation to themoss-lemming dynamics at Point Barrow. This, together with ourbifurcation analysis, indicates that neither seasonal factors(expressed by time-dependent moss growth rate and lemming death ratein the Barrow model) nor the moss growth rate and lemming death rateare the main culprits of the observed multi-year lemming cycles. Wesuspect that the main culprits may include high lemming predationrate, high lemming birth rate, and low lemming self-limitation rate.https://www.aimspress.com/article/doi/10.3934/mbe.2007.4.85functional responsepredator-prey modeloscillation. |
| spellingShingle | Hao Wang Yang Kuang Alternative models for cyclic lemming dynamics Mathematical Biosciences and Engineering functional response predator-prey model oscillation. |
| title | Alternative models for cyclic lemming dynamics |
| title_full | Alternative models for cyclic lemming dynamics |
| title_fullStr | Alternative models for cyclic lemming dynamics |
| title_full_unstemmed | Alternative models for cyclic lemming dynamics |
| title_short | Alternative models for cyclic lemming dynamics |
| title_sort | alternative models for cyclic lemming dynamics |
| topic | functional response predator-prey model oscillation. |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2007.4.85 |
| work_keys_str_mv | AT haowang alternativemodelsforcycliclemmingdynamics AT yangkuang alternativemodelsforcycliclemmingdynamics |