Journal of Mathematical Biology
, Volume 49, Issue 2, pp 188200
First online:
A stage structured predatorprey model and its dependence on maturation delay and death rate
 Stephen A. GourleyAffiliated withDepartment of Mathematics and Statistics, University of Surrey Email author
 , Yang KuangAffiliated withDepartment of Mathematics and Statistics, Arizona State University
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Many of the existing models on stage structured populations are single species models or models which assume a constant resource supply. In reality, growth is a combined result of birth and death processes, both of which are closely linked to the resource supply which is dynamic in nature. From this basic standpoint, we formulate a general and robust predatorprey model with stage structure with constant maturation time delay (throughstage time delay) and perform a systematic mathematical and computational study. Our work indicates that if the juvenile death rate (throughstage death rate) is nonzero, then for small and large values of maturation time delays, the population dynamics takes the simple form of a globally attractive steady state. Our linear stability work shows that if the resource is dynamic, as in nature, there is a window in maturation time delay parameter that generates sustainable oscillatory dynamics.
Key words or phrases:
Delay equation Stage structure Intraspecific competition Lyapunov functional Population model Throughstage death rate Title
 A stage structured predatorprey model and its dependence on maturation delay and death rate
 Journal

Journal of Mathematical Biology
Volume 49, Issue 2 , pp 188200
 Cover Date
 200408
 DOI
 10.1007/s0028500402782
 Print ISSN
 03036812
 Online ISSN
 14321416
 Publisher
 SpringerVerlag
 Additional Links
 Keywords

 Delay equation
 Stage structure
 Intraspecific competition
 Lyapunov functional
 Population model
 Throughstage death rate
 Industry Sectors
 Authors

 Stephen A. Gourley ^{(1)}
 Yang Kuang ^{(2)}
 Author Affiliations

 1. Department of Mathematics and Statistics, University of Surrey, Guildford, Surrey, GU2 7XH, UK
 2. Department of Mathematics and Statistics, Arizona State University, Tempe, AZ 85287, USA