Mathematical analysis of the asymptotic behavior of the Leslie population matrix model

1973 ◽  
Vol 35 (5-6) ◽  
pp. 645-661 ◽  
Author(s):  
Paul Cull ◽  
Andrew Vogt
Keyword(s):  
Asymptotic Behavior ◽  
Matrix Model ◽  
Mathematical Analysis ◽  
Population Matrix Model ◽  
Population Matrix

scholarly journals Another look at the eigenvalues of a population matrix model

PeerJ ◽  
2019 ◽  
Vol 7 ◽  
pp. e8018
Author(s):  
Brenda Hanley ◽  
Patrick Connelly ◽  
Brian Dennis
Keyword(s):  
Matrix Model ◽  
Dominant Eigenvalue ◽  
Interactive Software ◽  
Vital Rates ◽  
Finite Rate ◽  
Management Intervention ◽  
Rate Of Growth ◽  
Management Interventions ◽  
Population Matrix Model ◽  
Population Matrix

Population matrix models are important tools in resource management, in part because they are used to calculate the finite rate of growth (“dominant eigenvalue”). But understanding how a population matrix model converts life history traits into the finite rate of growth can be tricky. We introduce interactive software (“IsoPOPd”) that uses the characteristic equation to display how vital rates (survival and fertility) contribute to the finite rate of growth. Higher-order interactions among vital rates complicate the linkage between a management intervention and a population’s growth rate. We illustrate the use of the software for investigating the consequences of three management interventions in a 3-stage model of white-tailed deer (Odocoileus virginianus). The software is applicable to any species with 2- or 3-stages, but the mathematical concepts underlying the software are applicable to a population matrix model of any size. The IsoPOPd software is available at: https://cwhl.vet.cornell.edu/tools/isopopd.

scholarly journals Asymptotic Behavior and Critical Coupling in Scalar Yukawa Model

2018 ◽  
Vol 47 ◽  
pp. 1860095
Author(s):  
V. E. Rochev
Keyword(s):  
Asymptotic Behavior ◽  
Matrix Model ◽  
Critical Value ◽  
Leading Order ◽  
Coupling Constant ◽  
Critical Coupling ◽  
Yukawa Model ◽  
Four Dimensions ◽  
Euclidean Region ◽  
Vector Matrix

The solution of the equation for the pion propagator in the leading order of the [Formula: see text] – expansion for a vector-matrix model with interaction [Formula: see text] in four dimensions shows a change of the asymptotic behavior in the deep Euclidean region in a vicinity of a certain critical value of the coupling constant.

MATHEMATICAL ANALYSIS OF THE EVOLUTION OF A MODEL OF REGIONAL POPULATION DISTRIBUTION

2006 ◽  
Vol 16 (03) ◽  
pp. 347-374 ◽  
Author(s):  
J. EL GHORDAF ◽  
M. L. HBID
Keyword(s):  
Complex System ◽  
Asymptotic Behavior ◽  
Mathematical Analysis ◽  
Population Distribution ◽  
Extensive Study ◽  
Nonlinear Ordinary Differential Equations ◽  
Qualitative Properties ◽  
Urban Dynamics ◽  
First Order ◽  
Regional Population

This paper deals with the mathematical analysis of a model of urban dynamics, which was proposed by Miyata and Yamaguchi in the context of a region of Japan. The model is a complex system of first-order nonlinear ordinary differential equations. The study undertaken by Miyata and Yamaguchi is essentially computational, while an extensive study of the asymptotic behavior of the solutions is performed in this paper related to a detailed analysis of the qualitative properties of the system.

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