Abstract:
A coupled Gompertz-like system of delay differential equations is considered. We prove the existence of T-periodic solutions under resonance assuming a Lazer–Leach type condition. © 2018 Elsevier Ltd
Registro:
Documento: |
Artículo
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Título: | Lazer–Leach conditions for coupled Gompertz-like delayed systems |
Autor: | Amster, P.; Déboli, A.; Kuna, M.P. |
Filiación: | Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires. Ciudad Universitaria, Pabellón I, Buenos Aires (1428), Argentina IMAS-CONICET, Argentina Instituto de Ciencias, Universidad Nacional de General Sarmiento, Juan María Gutiérrez 1150, Los Polvorines, Buenos Aires (1613), Argentina
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Palabras clave: | Biological models; Delayed systems; Gompertz equation; Lazer–Leach conditions; Periodic solutions; Resonant problems; Topological degree methods; Differential equations; Topology; Biological models; Delayed systems; Gompertz equations; Periodic solution; Resonant problems; Topological degree methods; Leaching |
Año: | 2018
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Volumen: | 83
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Página de inicio: | 53
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Página de fin: | 58
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DOI: |
http://dx.doi.org/10.1016/j.aml.2018.03.013 |
Título revista: | Applied Mathematics Letters
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Título revista abreviado: | Appl Math Lett
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ISSN: | 08939659
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CODEN: | AMLEE
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Registro: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_08939659_v83_n_p53_Amster |
Referencias:
- Gompertz, G., On the nature of the function expressive of the law of human mortality, and on the new mode of determining the value of life contingencies (1825) Philos. Trans. R. Soc. Lond., 115, pp. 513-585
- Winsor, C.P., The Gompertz curve as a growth curve (1932) Proc. Natl. Acad. Sci. USA, pp. 1-7
- Laird, A.K., Dynamics of tumour growth (1964) Br. J. Cancer, 18 (3), pp. 490-502
- Laird, A.K., Dynamics of tumour growth: comparison of growth rates and extrapolation of growth curve to one cell (1965) Br. J. Cancer, 19, pp. 278-291
- Braverman, E., Mamdani, R., Continuous versus pulse harvesting for population models in constant and variable environment (2008) J. Math. Biol., 57, pp. 413-434
- Cohen, S.I., Vendruscolo, M., Dobson, C.M., Knowles, T.P., From macroscopic measurements to microscopic mechanisms of protein aggregation (2012) J. Mol. Biol., 421, pp. 160-171
- Zwietering, M.H., Jongenburger, I., Rombouts, F.M., Van't Riet, K., Modeling of the bacterial growth curve (1990) Appl. Environ. Microbiol., 56 (6), pp. 1875-1881
- Gomatam, J., A new model for interacting populations–I: Two-species systems (1974) Bull. Math. Biol., 36, pp. 347-353
- Li, Y., Cheng, H., Wang, J., Wang, Y., Dynamic analysis of unilateral diffusion Gompertz model with impulsive control strategy (2018) Adv. Difference Equ., pp. 32-46
- Supriatna, A.K., Husniah, H., Sustainable harvesting strategy for natural resources having a coupled Gompertz production function (2015) Interdisciplinary Behavior and Social Sciences: Proceedings of the 3rd International Congress on Interdisciplinary Behavior and Social Science, Vol. 2014, pp. 91-95. , CRC Press
- You, L., Zhao, Y., Optimal harvesting of a Gompertz population model with a marine protected area and interval-value biological parameters (2017) Math. Methods Appl. Sci., pp. 1-14
- Berezansky, L., Braverman, E., Idels, L., Effect of treatment on the global dynamics of delayed pathological angiogenesis models (2014) J. Theoret. Biol., 363, pp. 13-21
- Berezansky, L., Bunimovich-Mendrazitsky, A., Domoshnitsky, S., A mathematical model with time-varying delays in the combined treatment of chronic myeloid leukemia (2012) Adv. Difference Equ., pp. 217-230
- Jia, J., Li, C., A predator–prey Gompertz model with time delay and impulsive perturbations on the prey (2009) Discrete Dyn. Nat. Soc., 2009, pp. 1-15. , Article ID 256195
- Lazer, A., Leach, D., Bounded perturbations of forced harmonic oscillators at resonance (1969) Ann. Mat. Pura Appl., 82, pp. 49-68
- Amster, P., Idels, L., Existence theorems for some abstract nonlinear non-autonomous systems with delays (2014) Commun. Nonlinear Sci. Numer. Simul., 19, pp. 2974-2982
- Krasnoselskii, A.M., Mawhin, J., Periodic solutions of equations with oscillating nonlinearities (2000) Math. Comput. Modelling, 32 (11-13), pp. 1445-1455
Citas:
---------- APA ----------
Amster, P., Déboli, A. & Kuna, M.P.
(2018)
. Lazer–Leach conditions for coupled Gompertz-like delayed systems. Applied Mathematics Letters, 83, 53-58.
http://dx.doi.org/10.1016/j.aml.2018.03.013---------- CHICAGO ----------
Amster, P., Déboli, A., Kuna, M.P.
"Lazer–Leach conditions for coupled Gompertz-like delayed systems"
. Applied Mathematics Letters 83
(2018) : 53-58.
http://dx.doi.org/10.1016/j.aml.2018.03.013---------- MLA ----------
Amster, P., Déboli, A., Kuna, M.P.
"Lazer–Leach conditions for coupled Gompertz-like delayed systems"
. Applied Mathematics Letters, vol. 83, 2018, pp. 53-58.
http://dx.doi.org/10.1016/j.aml.2018.03.013---------- VANCOUVER ----------
Amster, P., Déboli, A., Kuna, M.P. Lazer–Leach conditions for coupled Gompertz-like delayed systems. Appl Math Lett. 2018;83:53-58.
http://dx.doi.org/10.1016/j.aml.2018.03.013