NDLI: Synchrony and the Dynamic Dichotomy in a Class of Matrix Population Models

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Veprauskas, A.
Copyright Year	2018
Abstract	Temporal synchronization in population dynamics is a common ecological phenomenon that can have important consequences for conservation and management strategies. Though many environmental factors may cause cycling, it is also possible for cycles to occur due to intrinsic properties of the population, such as competition between individuals at different developmental stages. For discrete-time matrix models, competition between stages may result in synchronous cycles in which stages are temporally separated. In this paper we define a class of matrix models which exhibit a simultaneous bifurcation of positive equilibria and synchronous 2-cycles when the extinction equilibrium destabilizes. We also show that a dynamic dichotomy exists between the two steady states such that, if the steady states are bifurcating forward, then they have opposite stability conditions. Which of the two steady states is stable depends on measures of the within-class and between-class competition. These results extend the fundamental bifurcation theorem to a class of matrix models whose inherent projection matrix has index of imprimitivity two.
Sponsorship	National Science Foundation
Starting Page	2491
Ending Page	2510
Page Count	20
File Format	PDF
ISSN	00361399
DOI	10.1137/17M1136444
e-ISSN	1095712X
Issue Number	5
Volume Number	78
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2018-09-18
Access Restriction	Subscribed
Subject Keyword	structured population dynamics fundamental bifurcation theorem bifurcation dynamic dichotomy Bifurcations of limit cycles and periodic orbits synchronous cycles Population dynamics imprimitive projection matrix models
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics

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