Global stability of almost periodic solutions in population dynamics
Authors:
Homero G. Díaz-Marín and Osvaldo Osuna
Journal:
Quart. Appl. Math. 81 (2023), 615-632
MSC (2020):
Primary 34C07, 34C27, 34D23, 92C37
DOI:
https://doi.org/10.1090/qam/1636
Published electronically:
October 20, 2022
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Additional Information
Abstract: We study first order differential equations with continuous almost periodic time dependence. We propose existence and global stability criteria of almost periodic solutions. Our results are specially useful in the study of one species population dynamics, such as logistic models with almost periodic parameters. Almost periodic time dependence also provides an explanation for oscillatory solutions in models of hematopoiesis disease dynamics.
References
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References
- Fred Brauer and Carlos Castillo-Chavez, Mathematical models in population biology and epidemiology, 2nd ed., Texts in Applied Mathematics, vol. 40, Springer, New York, 2012. MR 3024808, DOI 10.1007/978-1-4614-1686-9
- J. D. Murray, Mathematical biology. I, 3rd ed., Interdisciplinary Applied Mathematics, vol. 17, Springer-Verlag, New York, 2002. An introduction. MR 1908418
- M. Mackey and L. Glass, Oscillation and chaos in physiological control systems, Science 197 (1977), 287–289.
- L. Glass and M. Mackey, Pathological conditions resulting from instabilities in physiological control systems, Ann. N. Y. Acad. Science 316 (1979), 214–235.
- Shihe Xu, Qualitative analysis of a general periodic system, Commun. Korean Math. Soc. 33 (2018), no. 3, 1039–1048. MR 3846046, DOI 10.4134/CKMS.c170267
- Shandelle M. Henson and J. M. Cushing, The effect of periodic habitat fluctuations on a nonlinear insect population model, J. Math. Biol. 36 (1997), no. 2, 201–226. MR 1601788, DOI 10.1007/s002850050098
- Mihai Bostan, Almost periodic solutions for first-order differential equations, Differential Integral Equations 19 (2006), no. 1, 91–120. MR 2193965
- M. N. Nkashama, Dynamics of logistic equations with non-autonomous bounded coefficients, Electron. J. Differential Equations (2000), No. 02, 8. MR 1735059
- A. M. Fink, Almost periodic differential equations, Lecture Notes in Mathematics, Vol. 377, Springer-Verlag, Berlin-New York, 1974. MR 0460799
- Jack K. Hale, Ordinary differential equations, 2nd ed., Robert E. Krieger Publishing Co., Inc., Huntington, N.Y., 1980. MR 587488
- C. Corduneanu, Almost periodic functions, Chelsea Publishing Company, 2nd ed., 1989.
- P. Amster and R. Balderrama, On almost periodic solutions for a model of hematopoiesis with an oscillatory circulation loss rate, Math. Meth. Appl. Sci. 41 (2018), no. 10, 3976–3997.
- A. S. Besicovitch. Almost Periodic Functions, Cambridge University Press, 1932.
- Harald Bohr, Almost periodic functions, Chelsea Publishing Co., New York, N.Y., 1947. MR 0020163
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Additional Information
Homero G. Díaz-Marín
Affiliation:
Facultad de Ciencias Físico-Matemáticas, Universidad Michoacana. Edif. Alfa, Ciudad Universitaria, C.P. 58040. Morelia, Michoacán, México
ORCID:
0000-0002-2453-9049
Email:
homero.diaz@umich.mx
Osvaldo Osuna
Affiliation:
Instituto de Física y Matemáticas, Universidad Michoacana. Edif. C-3, Ciudad Universitaria, C.P. 58040. Morelia, Michoacán, México
MR Author ID:
761156
Email:
osvaldo.osuna@umich.mx
Keywords:
Global stability,
population dynamics,
almost periodic functions
Received by editor(s):
July 12, 2022
Received by editor(s) in revised form:
September 10, 2022
Published electronically:
October 20, 2022
Article copyright:
© Copyright 2022
Brown University
