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Awakened Oscillations in Coupled Consumer-Resource Pairs
Author
Source
Journal of Applied Mathematics
Issue
Vol. 2014, Issue 2014 (31 Dec. 2014), pp.1-20, 20 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2014-09-10
Country of Publication
Egypt
No. of Pages
20
Main Subjects
Abstract EN
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.
American Psychological Association (APA)
Mustafin, Almaz. 2014. Awakened Oscillations in Coupled Consumer-Resource Pairs. Journal of Applied Mathematics،Vol. 2014, no. 2014, pp.1-20.
https://search.emarefa.net/detail/BIM-1039728
Modern Language Association (MLA)
Mustafin, Almaz. Awakened Oscillations in Coupled Consumer-Resource Pairs. Journal of Applied Mathematics No. 2014 (2014), pp.1-20.
https://search.emarefa.net/detail/BIM-1039728
American Medical Association (AMA)
Mustafin, Almaz. Awakened Oscillations in Coupled Consumer-Resource Pairs. Journal of Applied Mathematics. 2014. Vol. 2014, no. 2014, pp.1-20.
https://search.emarefa.net/detail/BIM-1039728
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1039728