Awakened Oscillations in Coupled Consumer-Resource Pairs
The paper concerns two interacting consumer-resource pairs based on chemostat-like equations under the assumption that the dynamics of the resource is considerably slower than that of the consumer. The presence of two different time scales enables to carry out a fairly complete analysis of the probl...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2014/561958 |
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| _version_ | 1832551017865019392 |
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| author | Almaz Mustafin |
| author_facet | Almaz Mustafin |
| author_sort | Almaz Mustafin |
| collection | DOAJ |
| description | The paper concerns two interacting consumer-resource pairs based on chemostat-like equations under the assumption that the dynamics of the resource is considerably slower than that of the consumer. The presence of two different time scales enables to carry out a fairly complete analysis of the problem. This is done by treating consumers and resources in the coupled system as fast-scale and slow-scale variables, respectively, and subsequently considering developments in phase planes of these variables, fast and slow, as if they are independent. When uncoupled, each pair has unique asymptotically stable steady state and no self-sustained oscillatory behavior (although damped oscillations about the equilibrium are admitted). When the consumer-resource pairs are weakly coupled through direct reciprocal inhibition of consumers, the whole system exhibits self-sustained relaxation oscillations with a period that can be significantly longer than intrinsic relaxation time of either pair. It is shown that the model equations adequately describe locally linked consumer-resource systems of quite different nature: living populations under interspecific interference competition and lasers coupled via their cavity losses. |
| format | Article |
| id | doaj-art-f8e6738f41d34b74a710b06095e4a676 |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-f8e6738f41d34b74a710b06095e4a6762025-02-03T06:05:21ZengWileyJournal of Applied Mathematics1110-757X1687-00422014-01-01201410.1155/2014/561958561958Awakened Oscillations in Coupled Consumer-Resource PairsAlmaz Mustafin0Department of General and Theoretical Physics, Kazakh National Technical University, 22 Satpayev Street, Almaty 050013, KazakhstanThe paper concerns two interacting consumer-resource pairs based on chemostat-like equations under the assumption that the dynamics of the resource is considerably slower than that of the consumer. The presence of two different time scales enables to carry out a fairly complete analysis of the problem. This is done by treating consumers and resources in the coupled system as fast-scale and slow-scale variables, respectively, and subsequently considering developments in phase planes of these variables, fast and slow, as if they are independent. When uncoupled, each pair has unique asymptotically stable steady state and no self-sustained oscillatory behavior (although damped oscillations about the equilibrium are admitted). When the consumer-resource pairs are weakly coupled through direct reciprocal inhibition of consumers, the whole system exhibits self-sustained relaxation oscillations with a period that can be significantly longer than intrinsic relaxation time of either pair. It is shown that the model equations adequately describe locally linked consumer-resource systems of quite different nature: living populations under interspecific interference competition and lasers coupled via their cavity losses.http://dx.doi.org/10.1155/2014/561958 |
| spellingShingle | Almaz Mustafin Awakened Oscillations in Coupled Consumer-Resource Pairs Journal of Applied Mathematics |
| title | Awakened Oscillations in Coupled Consumer-Resource Pairs |
| title_full | Awakened Oscillations in Coupled Consumer-Resource Pairs |
| title_fullStr | Awakened Oscillations in Coupled Consumer-Resource Pairs |
| title_full_unstemmed | Awakened Oscillations in Coupled Consumer-Resource Pairs |
| title_short | Awakened Oscillations in Coupled Consumer-Resource Pairs |
| title_sort | awakened oscillations in coupled consumer resource pairs |
| url | http://dx.doi.org/10.1155/2014/561958 |
| work_keys_str_mv | AT almazmustafin awakenedoscillationsincoupledconsumerresourcepairs |