Document Detail


Seasonal forcing and multi-year cycles in interacting populations: lessons from a predator-prey model.
MedLine Citation:
PMID:  23138231     Owner:  NLM     Status:  Publisher    
Abstract/OtherAbstract:
Many natural systems are subject to seasonal environmental change. As a consequence many species exhibit seasonal changes in their life history parameters-such as a peak in the birth rate in spring. It is important to understand how this seasonal forcing affects the population dynamics. The main way in which seasonal models have been studied is through a two dimensional bifurcation approach. We augment this bifurcation approach with extensive simulation in order to understand the potential solution behaviours for a predator-prey system with a seasonally forced prey growth rate. We consider separately how forcing influences the system when the unforced dynamics have either monotonic decay to the coexistence steady state, or oscillatory decay, or stable limit cycles. The range of behaviour the system can exhibit includes multi-year cycles of different periodicities, parameter ranges with coexisting multi-year cycles of the same or different period as well as quasi-periodicity and chaos. We show that the level of oscillation in the unforced system has a large effect on the range of behaviour when the system is seasonally forced. We discuss how the methods could be extended to understand the dynamics of a wide range of ecological and epidemiological systems that are subject to seasonal changes.
Authors:
Rachel A Taylor; Jonathan A Sherratt; Andrew White
Publication Detail:
Type:  JOURNAL ARTICLE     Date:  2012-11-9
Journal Detail:
Title:  Journal of mathematical biology     Volume:  -     ISSN:  1432-1416     ISO Abbreviation:  J Math Biol     Publication Date:  2012 Nov 
Date Detail:
Created Date:  2012-11-9     Completed Date:  -     Revised Date:  -    
Medline Journal Info:
Nlm Unique ID:  7502105     Medline TA:  J Math Biol     Country:  -    
Other Details:
Languages:  ENG     Pagination:  -     Citation Subset:  -    
Affiliation:
Department of Mathematics and the Maxwell Institute for Mathematical Sciences, Heriot-Watt University, Edinburgh, EH14 4AS, UK, rat3@hw.ac.uk.
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