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A unifying approach to discrete single-species populations models
Department of Mathematics and Statistics, Georgetown University, Washington, DC 20057-1233, USA |
$f$ |
$p_{n+1} =f(p_n)$ |
$f(p) =p+r(p)p$ |
$r$ |
$r$ |
$f$ |
$r$ |
$f$ |
References:
[1] |
T. S. Bellows,
The descriptive properties of some models for density dependence, Journal of Animal Ecology, 50 (1981), 139-156.
doi: 10.2307/4037. |
[2] |
R. J. H. Beverton and S. J. Holt, On the Dynamics of Exploited Fish Populations, Fish & Fisheries Series, 1993.
doi: 10.1007/978-94-011-2106-4. |
[3] |
P. Cull,
Population models: Stability in one dimension, Bulletin Mathematical Biology, 69 (2007), 989-1017.
doi: 10.1007/s11538-006-9129-1. |
[4] |
M. P. Hassell,
Density dependence in single-species populations, Journal of Animal Ecology, 44 (1975), 283-295.
doi: 10.2307/3863. |
[5] |
R. J. Higgins, C. M. Kent, V. L. Kocic and Y. Kostrov,
Dynamics of a nonlinear discrete population model with jumps, Applicable Analysis and Discrete Mathematics, 9 (2015), 245-270.
doi: 10.2298/AADM150930019H. |
[6] |
V. L. Kocic and Y. Kostrov,
Dynamics of a discontinuous discrete Beverton-Holt model, Journal of Difference Equations and Applications, 20 (2014), 859-874.
doi: 10.1080/10236198.2013.824968. |
[7] |
M. Liermann and R. Hilborn,
Depensation: Evidence, models and implications, Fish and Fisheries, 2 (2001), 33-58.
|
[8] |
J. Maynard-smith and M. Slatkin,
The stability of predator-prey systems, Ecology, 54 (1973), 384-391.
|
[9] |
R. M. May,
Simple mathematical models with very complicated dynamics, The Theory of Chaotic Attractors, (2004), 85-93.
doi: 10.1007/978-0-387-21830-4_7. |
[10] |
W. E. Ricker,
Stock and recruitment, Journal of the Fisheries Research Board of Canada, 11 (1954), 559-623.
doi: 10.1139/f54-039. |
[11] |
J. T. Sandefur, Discrete Dynamical Systems: Theory and Applications, Oxford University Press, Oxford, 1990. |
[12] |
M. Williamson, The analysis of discrete time cycles, Ecological stability (eds. M. B. Usher and Author), Chapman and Hall, (1974), 17–33.
doi: 10.1007/978-1-4899-6938-5_2. |
show all references
References:
[1] |
T. S. Bellows,
The descriptive properties of some models for density dependence, Journal of Animal Ecology, 50 (1981), 139-156.
doi: 10.2307/4037. |
[2] |
R. J. H. Beverton and S. J. Holt, On the Dynamics of Exploited Fish Populations, Fish & Fisheries Series, 1993.
doi: 10.1007/978-94-011-2106-4. |
[3] |
P. Cull,
Population models: Stability in one dimension, Bulletin Mathematical Biology, 69 (2007), 989-1017.
doi: 10.1007/s11538-006-9129-1. |
[4] |
M. P. Hassell,
Density dependence in single-species populations, Journal of Animal Ecology, 44 (1975), 283-295.
doi: 10.2307/3863. |
[5] |
R. J. Higgins, C. M. Kent, V. L. Kocic and Y. Kostrov,
Dynamics of a nonlinear discrete population model with jumps, Applicable Analysis and Discrete Mathematics, 9 (2015), 245-270.
doi: 10.2298/AADM150930019H. |
[6] |
V. L. Kocic and Y. Kostrov,
Dynamics of a discontinuous discrete Beverton-Holt model, Journal of Difference Equations and Applications, 20 (2014), 859-874.
doi: 10.1080/10236198.2013.824968. |
[7] |
M. Liermann and R. Hilborn,
Depensation: Evidence, models and implications, Fish and Fisheries, 2 (2001), 33-58.
|
[8] |
J. Maynard-smith and M. Slatkin,
The stability of predator-prey systems, Ecology, 54 (1973), 384-391.
|
[9] |
R. M. May,
Simple mathematical models with very complicated dynamics, The Theory of Chaotic Attractors, (2004), 85-93.
doi: 10.1007/978-0-387-21830-4_7. |
[10] |
W. E. Ricker,
Stock and recruitment, Journal of the Fisheries Research Board of Canada, 11 (1954), 559-623.
doi: 10.1139/f54-039. |
[11] |
J. T. Sandefur, Discrete Dynamical Systems: Theory and Applications, Oxford University Press, Oxford, 1990. |
[12] |
M. Williamson, The analysis of discrete time cycles, Ecological stability (eds. M. B. Usher and Author), Chapman and Hall, (1974), 17–33.
doi: 10.1007/978-1-4899-6938-5_2. |











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