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Abstract:

Using topological degree theory, we prove the existence of positive periodic solutions of a system of delay differential equations for models with feedback arising on regulatory mechanisms in which self-regulation is relevant, e.g. in cell physiology. We study different models based on the cycle of testosterone and generalizations. The method in the present work allows to analyse and extend known results from a different perspective, shortening proofs and giving an alternative approach for the study of complex models. © 2018 Elsevier B.V.

Registro:

Documento: Artículo
Título:Systems of delay differential equations: Analysis of a model with feedback
Autor:Alliera, C.H.D.; Amster, P.
Filiación:Departamento de Matemática, FCEyN - Universidad de Buenos Aires, Pabellón I, Ciudad Universitaria, Buenos Aires, Argentina
IMAS-CONICET, Argentina
Palabras clave:Models with feedback; Periodic solutions; Systems of DDEs; Cytology; Physiology; Problem solving; Topology; Cell physiology; Complex model; Delay differential equations; Existence of positive periodic solutions; Periodic solution; Regulatory mechanism; Self regulation; Topological degree theory; Differential equations
Año:2018
Volumen:65
Página de inicio:299
Página de fin:308
DOI: http://dx.doi.org/10.1016/j.cnsns.2018.05.021
Título revista:Communications in Nonlinear Science and Numerical Simulation
Título revista abreviado:Comm. Nonlinear Sci. Numer. Simul.
ISSN:10075704
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_10075704_v65_n_p299_Alliera

Referencias:

  • 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
  • Amster, P., Idels, L., Periodic solutions in general scalar non-autonomous models with delays (2013) Nonlinear Differ Equ Appl NoDEA, 20, pp. 1577-1596
  • Blache, D., Zhang, S., Martin, G., Fertility in male sheep: modulators of the acute effects of nutrition on the reproductive axis of male sheep (2003) Reprod Suppl, 61, pp. 823-829
  • Cartwright, M., Husain, M., A model for the control of testosterone secretion (1986) J Theor Biol, 123, pp. 239-250
  • Das, P., Roy, A.B., Das, A., Stability and oscillations of a negative feedback delay model for the control of testosterone secretion (1994) BioSystems, 32, pp. 61-69
  • Ferasyi, T., Barrett, R., Blache, D., Martin, G., Modeling the male reproductive endocrine axis: potential role for a delay mechanism in the inhibitory action of gonadal steroids on gnRH pulse frequency (2016) Endocrinology, 157, pp. 2080-2092
  • Goldbeter, A., Biochemical oscillations and cellular rhythms (1996), Cambridge University Press; Goodwin, B., Oscillatory behaviour in enzymatic control processes (1965) Adv Enzyme Regul, 3, pp. 425-438
  • Greenhalgh, D., Khan, Q.J.A., A delay differential equation mathematical model for the control of the hormonal system of the hypothalamus, the pituitary and the testis in man (2009) Nonlinear Anal Theory Methods Appl, 71 (12), pp. 925-935
  • Hastings, S., Tyson, J., Webster, D., Existence of periodic solutions for negative feedback cellular control systems (1976) J Differ Equ, 25, pp. 39-64
  • Liu, B., Deng, G., An improved mathematical model of hormone secretion in the hypothalamo–pituitary–gonadal axis in man (1991) J Theor Biol, 150, pp. 51-58
  • Murray, J., Mathematical biology. I. An introduction (2001), Springer New York; Ruan, S., Wei, J., On the zeros of a third degree exponential polynomial with applications to a delayed model for the control of testosterone secretion (2001) IMA J Math Appl Med Biol, 18, pp. 41-52
  • Smith, W., Hypothalamic regulation of pituitary secretion of luteinizing hormone. II. Feedback control of gonadotropin secretion (1980) Bull Math Biol, 42, pp. 57-78

Citas:

---------- APA ----------
Alliera, C.H.D. & Amster, P. (2018) . Systems of delay differential equations: Analysis of a model with feedback. Communications in Nonlinear Science and Numerical Simulation, 65, 299-308.
http://dx.doi.org/10.1016/j.cnsns.2018.05.021
---------- CHICAGO ----------
Alliera, C.H.D., Amster, P. "Systems of delay differential equations: Analysis of a model with feedback" . Communications in Nonlinear Science and Numerical Simulation 65 (2018) : 299-308.
http://dx.doi.org/10.1016/j.cnsns.2018.05.021
---------- MLA ----------
Alliera, C.H.D., Amster, P. "Systems of delay differential equations: Analysis of a model with feedback" . Communications in Nonlinear Science and Numerical Simulation, vol. 65, 2018, pp. 299-308.
http://dx.doi.org/10.1016/j.cnsns.2018.05.021
---------- VANCOUVER ----------
Alliera, C.H.D., Amster, P. Systems of delay differential equations: Analysis of a model with feedback. Comm. Nonlinear Sci. Numer. Simul. 2018;65:299-308.
http://dx.doi.org/10.1016/j.cnsns.2018.05.021