Oscillation and stability in a simple genotype selection model
Authors:
E. A. Grove, V. Lj. Kocić, G. Ladas and R. Levins
Journal:
Quart. Appl. Math. 52 (1994), 499-508
MSC:
Primary 92D10; Secondary 39A12
DOI:
https://doi.org/10.1090/qam/1292200
MathSciNet review:
MR1292200
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Abstract: We study the oscillation, the stability, and the global attractivity of the simple genotype selection model \[ {y_{n + 1}} = \frac {{{y_n}{e^{\beta \left ( 1 - 2{y_{n - k}}\right )}}}}{{1 - {y_n} + {y_n}{e^{\beta \left (1 - 2{y_{n - k}} \right )}}}}, \qquad n = 0, 1,...,\] where $\beta \in \left ( 0, \infty \right )$ and $k \in \{ 0, 1, 2,...\}$.
P. Cull, Global stability of population models, Bull. Math. Biol. 43, 47–58 (1981)
P. Cull, Stability of discrete one-dimensional population models, Bull. Math. Biol. 50, 67–75 (1988)
M. E. Fisher, B. S. Goh, and T. L. Vincent, Some stability conditions for discrete-time single species models, Bull. Math. Biol. 41, 861–875 (1979)
I. Györi and G. Ladas, Oscillation Theory of Delay Differenial Equations with Applications, Clarendon Press, Oxford, 1991
Y. Huang, A note on stability of discrete population models, Math. Biosci. 95, 189–198 (1989)
J. H. Jaroma, V. Lj. Kocić, and G. Ladas, Global asymptotic stability of a second-order difference equation, Partial Differential Equations (J. Wiener and J. K. Hale, eds.), Pitman Research Notes in Mathematics Series, no. 273, Longman Scientific and Technical, 1992, pp. 80–84
V. Lj. Kocić and G. Ladas, Global attractivity in nonlinear delay difference equations, Proc. Amer. Math. Soc. 115, 1083–1088 (1992)
S. Levin and R. May, A note on difference-delay equations, Theoret. Population Biol. 9, 178–187 (1976)
R. M. May, Nonlinear problems in ecology and resource management, Course 8 in Chaotic Behaviour of Deterministic Systems (G. Iooss, R. H. G. Helleman, and R. Stora, eds.), North-Holland, Amsterdam, 1983
G. Rosenkranz, On global stability of discrete population models, Math. Biosci. 64, 227–231 (1983)
P. Cull, Global stability of population models, Bull. Math. Biol. 43, 47–58 (1981)
P. Cull, Stability of discrete one-dimensional population models, Bull. Math. Biol. 50, 67–75 (1988)
M. E. Fisher, B. S. Goh, and T. L. Vincent, Some stability conditions for discrete-time single species models, Bull. Math. Biol. 41, 861–875 (1979)
I. Györi and G. Ladas, Oscillation Theory of Delay Differenial Equations with Applications, Clarendon Press, Oxford, 1991
Y. Huang, A note on stability of discrete population models, Math. Biosci. 95, 189–198 (1989)
J. H. Jaroma, V. Lj. Kocić, and G. Ladas, Global asymptotic stability of a second-order difference equation, Partial Differential Equations (J. Wiener and J. K. Hale, eds.), Pitman Research Notes in Mathematics Series, no. 273, Longman Scientific and Technical, 1992, pp. 80–84
V. Lj. Kocić and G. Ladas, Global attractivity in nonlinear delay difference equations, Proc. Amer. Math. Soc. 115, 1083–1088 (1992)
S. Levin and R. May, A note on difference-delay equations, Theoret. Population Biol. 9, 178–187 (1976)
R. M. May, Nonlinear problems in ecology and resource management, Course 8 in Chaotic Behaviour of Deterministic Systems (G. Iooss, R. H. G. Helleman, and R. Stora, eds.), North-Holland, Amsterdam, 1983
G. Rosenkranz, On global stability of discrete population models, Math. Biosci. 64, 227–231 (1983)
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Article copyright:
© Copyright 1994
American Mathematical Society
