Bulletin of Mathematical Biology
, Volume 65, Issue 3, pp 479495
First online:
Multiple attractors in stagestructured population models with birth pulses
 Sanyi TangAffiliated withInstitute of Mathematics, Academy of Mathematics and System Sciences, Academia Sinica Email author
 , Lansun ChenAffiliated withInstitute of Mathematics, Academy of Mathematics and System Sciences, Academia Sinica
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In most models of population dynamics, increases in population due to birth are assumed to be timeindependent, but many species reproduce only during a single period of the year. A single species stagestructured model with densitydependent maturation rate and birth pulse is formulated. Using the discrete dynamical system determined by its Poincaré map, we report a detailed study of the various dynamics, including (a) existence and stability of nonnegative equilibria, (b) nonunique dynamics, meaning that several attractors coexist, (c) basins of attraction (defined as the set of the initial conditions leading to a certain type of attractor), (d) supertransients, and (e) chaotic attractors. The occurrence of these complex dynamic behaviour is related to the fact that minor changes in parameter or initial values can strikingly change the dynamic behaviours of system. Further, it is shown that periodic birth pulse, in effect, provides a natural period or cyclicity that allows multiple oscillatory solutions in the continuous dynamical systems.
 Title
 Multiple attractors in stagestructured population models with birth pulses
 Journal

Bulletin of Mathematical Biology
Volume 65, Issue 3 , pp 479495
 Cover Date
 200305
 DOI
 10.1016/S00928240(03)000053
 Print ISSN
 00928240
 Online ISSN
 15229602
 Publisher
 SpringerVerlag
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 Authors

 Sanyi Tang ^{(1)}
 Lansun Chen ^{(1)}
 Author Affiliations

 1. Institute of Mathematics, Academy of Mathematics and System Sciences, Academia Sinica, Beijing, 100080, People’s Republic of China