Dynamics of Planar Systems That Model Stage-Structured Populations
We study a general discrete planar system for modeling stage-structured populations. Our results include conditions for the global convergence of orbits to zero (extinction) when the parameters (vital rates) are time and density dependent. When the parameters are periodic we obtain weaker conditions...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2015-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2015/137182 |
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| Summary: | We study a general discrete planar system for modeling stage-structured
populations. Our results include conditions for the global convergence of
orbits to zero (extinction) when the parameters (vital rates) are time and density dependent. When the parameters are
periodic we obtain weaker conditions for extinction. We also study a rational
special case of the system for Beverton-Holt type interactions and show that
the persistence equilibrium (in the positive quadrant) may be globally
attracting even in the presence of interstage competition. However, we
determine that with a sufficiently high level of competition, the persistence equilibrium becomes unstable (a saddle point) and the system exhibits period two
oscillations. |
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| ISSN: | 1026-0226 1607-887X |