Study of the Existence of Global Attractors for the Wezewska, Czyewska and Lasota Models

Edgar Alí Medina; Manuel Vicente Centeno-Romero; Fernando José Marval López; José Feliciano Lockiby Aguirre

doi:doi:10.11648/j.ml.20210703.11

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Study of the Existence of Global Attractors for the Wezewska, Czyewska and Lasota Models

Edgar Alí Medina, Manuel Vicente Centeno-Romero, Fernando José Marval López, José Feliciano Lockiby Aguirre

Published in Mathematics Letters (Volume 7, Issue 3)

Received: 8 May 2021 Accepted: 21 July 2021 Published: 31 August 2021

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Abstract

In this research we present a study of global attractors in mathematical models of differential equations, which are an important tool in mathematics; furthermore, taking advantage of the stability of the solutions, it was possible to determine the control of biomedical phenomena, among other aspects, present in various population groups. Likewise, differential equation models are used to simulate biological, epidemiological and medical phenomena, among others. The reference population groups used in this research are the family of population models given by the differential equations N'(t)=p(t, N (t)) - d(t, N (t)). A particular case of this family of differential equations is the mathematical model called the Wezewska, Czyewska and Lasota (WCL) model, whose form is given by: N'(t)=pe^(-q) - μN (t). This model describes the survival of red blood cells (erythrocytes) in humans. The WCL model, in discrete variable, has a non-trivial global attractor. In this research we demonstrate, using the Schwarz derivative technique, the existence of at least one model global attractor. On the other hand, the results of the present investigation showed the existence of a single fixed point, as the only global attractor characterized by the equation N=pe^(-qN) - μN.

Published in	Mathematics Letters (Volume 7, Issue 3)
DOI	10.11648/j.ml.20210703.11
Page(s)	37-40
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Global Attractor, Point Balances, Differential Equations, Fixed Point

References

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[2]	Medina, E. A. 2013. Equivalencia asintótica relativa de ecuaciones en diferencia. Trabajo de Ascenso para optar a la Categoría de Profesor Titular UDO. Venezuela.
[3]	Braverman, E. and Saker, S. H. 2011. On a Difference Equation with Exponentially Decreasing Nonlinearity. Hindawi Publishing Corporation Discrete Dynamics in Nature and Society 2011, Article ID 147926, 17 pages doi: 10.1155/2011/147926.
[4]	Bonotto, E. M., Bortolan, M. C., Carvalho, A. N. and Czaja, R. 2015. Global attractors for impulsive dynamical systems-a precompact approach. Journal of Differential Equations. 259 (7): 2602-2625.
[5]	Chi, P., Yuncheng, Y. and Jianzhong, S. 2019. Global attractors for Hindmarsh. Rose equations in Neurodynamics. Cornell University. Mathematics, Analysis of PDEs: 1907. 13225.
[6]	Lee, J., Nguyen, N. and Toi, Vu M. 2020. Gromov-Hausdorff stability of global attractors of reaction diffusion equations under perturbations of the domain. 269 (1): 125-147.
[7]	Yirong, J., Nanjing, H. and Nanjing, H. 2020. American Institute of Mathematical Sciences. 2584: 1193-1212.
[8]	Rangel, G. 2019. Global Attractors in Partial Differential Equations. CNRS et Universit´e de Paris-Sud Analyse Num´erique et EDP, UMR 8628. Bˆatiment 425. F-91405 Orsay Cedex, France. Genevieve.
[9]	Li, Y., Wang, Y. and Li, B. 2020. Existence and finite-time stability of a unique almost periodic positive solutionfor fractional-order Lasota-Wazewska red blood cell models. International Journal of Biomathematics. 13 (2).
[10]	Stamov, G. and Stamova, I. 2019. Impulsive Delayed Lasota–Wazewska Fractional Models: Global Stability of Integral Manifolds. Mathematics 7, 1025; doi: 10.3390.
[11]	Losson, J., Mackey, M. C. and Longtin, A. 1993. Solution multistability in first-order nonlinear differential delay equations. Chaos 3 (2): 167-176.
[12]	Mackey, M. C. and Glass, L. 1977. Oscillation and chaos in physiological control systems. Science 197 (4300): 287-289.
[13]	Medina, E. A., Centeno-Romero, M. V. y Marval, F. J. 2019. Global stability of critical points for type SIS epidemiological model. International Journal of Theoretical and Applied Mathematics 5 (6): 94-99.
[14]	Medina, E. A. 2016. Equivalencia Asintótica Relativa de Ecuaciones en Diferencia. Tesis Doctoral. Universidad Central de Venezuela. Caracas. Venezuela.
[15]	Rigalli, A., Aguirre C., Armendáriz, M. y Cassiraga, G. 2003. Formulación de modelos matemáticos de fenómenos biológicos. Doctorado en Ciencias Biomédicas, Facultad de Ciencias Médicas. Rosario, Argentina.
[16]	Franco, D., Guiver, Ch. Logemann, H. and Perán, J. 2020. On the global attractors of delay differential equations with unimodal feedback not satisfyins the negative schwarzian derivatie condition. Electronic Journal of Qualitative Theory of Differential equations. (76): 1-15.
[17]	Farji-Brener, A. G. 2007. Una forma alternativa para la enseñanza del método hipotético-deductivo. INCI 32 (10) ISSN 0378–1844.
[18]	Tamayo y Tamayo, M. 2011. El Proceso de la Investigación Científica. Editorial Limusa, S. A. de C. V. Grupo Noriega Editores. México.

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APA Style

Edgar Alí Medina, Manuel Vicente Centeno-Romero, Fernando José Marval López, José Feliciano Lockiby Aguirre. (2021). Study of the Existence of Global Attractors for the Wezewska, Czyewska and Lasota Models. Mathematics Letters, 7(3), 37-40. https://doi.org/10.11648/j.ml.20210703.11

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ACS Style

Edgar Alí Medina; Manuel Vicente Centeno-Romero; Fernando José Marval López; José Feliciano Lockiby Aguirre. Study of the Existence of Global Attractors for the Wezewska, Czyewska and Lasota Models. Math. Lett. 2021, 7(3), 37-40. doi: 10.11648/j.ml.20210703.11

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AMA Style

Edgar Alí Medina, Manuel Vicente Centeno-Romero, Fernando José Marval López, José Feliciano Lockiby Aguirre. Study of the Existence of Global Attractors for the Wezewska, Czyewska and Lasota Models. Math Lett. 2021;7(3):37-40. doi: 10.11648/j.ml.20210703.11

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@article{10.11648/j.ml.20210703.11,
  author = {Edgar Alí Medina and Manuel Vicente Centeno-Romero and Fernando José Marval López and José Feliciano Lockiby Aguirre},
  title = {Study of the Existence of Global Attractors for the Wezewska, Czyewska and Lasota Models},
  journal = {Mathematics Letters},
  volume = {7},
  number = {3},
  pages = {37-40},
  doi = {10.11648/j.ml.20210703.11},
  url = {https://doi.org/10.11648/j.ml.20210703.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ml.20210703.11},
  abstract = {In this research we present a study of global attractors in mathematical models of differential equations, which are an important tool in mathematics; furthermore, taking advantage of the stability of the solutions, it was possible to determine the control of biomedical phenomena, among other aspects, present in various population groups. Likewise, differential equation models are used to simulate biological, epidemiological and medical phenomena, among others. The reference population groups used in this research are the family of population models given by the differential equations N'(t)=p(t, N (t)) - d(t, N (t)). A particular case of this family of differential equations is the mathematical model called the Wezewska, Czyewska and Lasota (WCL) model, whose form is given by: N'(t)=pe(-q) - μN (t). This model describes the survival of red blood cells (erythrocytes) in humans. The WCL model, in discrete variable, has a non-trivial global attractor. In this research we demonstrate, using the Schwarz derivative technique, the existence of at least one model global attractor. On the other hand, the results of the present investigation showed the existence of a single fixed point, as the only global attractor characterized by the equation N=pe(-qN) - μN.},
 year = {2021}
}

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TY  - JOUR
T1  - Study of the Existence of Global Attractors for the Wezewska, Czyewska and Lasota Models
AU  - Edgar Alí Medina
AU  - Manuel Vicente Centeno-Romero
AU  - Fernando José Marval López
AU  - José Feliciano Lockiby Aguirre
Y1  - 2021/08/31
PY  - 2021
N1  - https://doi.org/10.11648/j.ml.20210703.11
DO  - 10.11648/j.ml.20210703.11
T2  - Mathematics Letters
JF  - Mathematics Letters
JO  - Mathematics Letters
SP  - 37
EP  - 40
PB  - Science Publishing Group
SN  - 2575-5056
UR  - https://doi.org/10.11648/j.ml.20210703.11
AB  - In this research we present a study of global attractors in mathematical models of differential equations, which are an important tool in mathematics; furthermore, taking advantage of the stability of the solutions, it was possible to determine the control of biomedical phenomena, among other aspects, present in various population groups. Likewise, differential equation models are used to simulate biological, epidemiological and medical phenomena, among others. The reference population groups used in this research are the family of population models given by the differential equations N'(t)=p(t, N (t)) - d(t, N (t)). A particular case of this family of differential equations is the mathematical model called the Wezewska, Czyewska and Lasota (WCL) model, whose form is given by: N'(t)=pe(-q) - μN (t). This model describes the survival of red blood cells (erythrocytes) in humans. The WCL model, in discrete variable, has a non-trivial global attractor. In this research we demonstrate, using the Schwarz derivative technique, the existence of at least one model global attractor. On the other hand, the results of the present investigation showed the existence of a single fixed point, as the only global attractor characterized by the equation N=pe(-qN) - μN.
VL  - 7
IS  - 3
ER  -

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Author Information

Edgar Alí Medina

Departamento de Ciencias, Universidad de Oriente Núcleo de Nueva Esparta, Guatamare, Venezuela
Manuel Vicente Centeno-Romero

Departamento de Matemáticas, Escuela de Ciencias, Universidad de Oriente Núcleo de Sucre, Cumaná, Venezuela
Fernando José Marval López

Departamento de Matemáticas, Escuela de Ciencias, Universidad de Oriente Núcleo de Sucre, Cumaná, Venezuela
José Feliciano Lockiby Aguirre

Departamento de Informática, Escuela de Ciencias, Universidad de Oriente Núcleo de Sucre, Cumaná, Venezuela

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APA Style

Edgar Alí Medina, Manuel Vicente Centeno-Romero, Fernando José Marval López, José Feliciano Lockiby Aguirre. (2021). Study of the Existence of Global Attractors for the Wezewska, Czyewska and Lasota Models. Mathematics Letters, 7(3), 37-40. https://doi.org/10.11648/j.ml.20210703.11

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ACS Style

Edgar Alí Medina; Manuel Vicente Centeno-Romero; Fernando José Marval López; José Feliciano Lockiby Aguirre. Study of the Existence of Global Attractors for the Wezewska, Czyewska and Lasota Models. Math. Lett. 2021, 7(3), 37-40. doi: 10.11648/j.ml.20210703.11

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AMA Style

Edgar Alí Medina, Manuel Vicente Centeno-Romero, Fernando José Marval López, José Feliciano Lockiby Aguirre. Study of the Existence of Global Attractors for the Wezewska, Czyewska and Lasota Models. Math Lett. 2021;7(3):37-40. doi: 10.11648/j.ml.20210703.11

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@article{10.11648/j.ml.20210703.11,
  author = {Edgar Alí Medina and Manuel Vicente Centeno-Romero and Fernando José Marval López and José Feliciano Lockiby Aguirre},
  title = {Study of the Existence of Global Attractors for the Wezewska, Czyewska and Lasota Models},
  journal = {Mathematics Letters},
  volume = {7},
  number = {3},
  pages = {37-40},
  doi = {10.11648/j.ml.20210703.11},
  url = {https://doi.org/10.11648/j.ml.20210703.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ml.20210703.11},
  abstract = {In this research we present a study of global attractors in mathematical models of differential equations, which are an important tool in mathematics; furthermore, taking advantage of the stability of the solutions, it was possible to determine the control of biomedical phenomena, among other aspects, present in various population groups. Likewise, differential equation models are used to simulate biological, epidemiological and medical phenomena, among others. The reference population groups used in this research are the family of population models given by the differential equations N'(t)=p(t, N (t)) - d(t, N (t)). A particular case of this family of differential equations is the mathematical model called the Wezewska, Czyewska and Lasota (WCL) model, whose form is given by: N'(t)=pe(-q) - μN (t). This model describes the survival of red blood cells (erythrocytes) in humans. The WCL model, in discrete variable, has a non-trivial global attractor. In this research we demonstrate, using the Schwarz derivative technique, the existence of at least one model global attractor. On the other hand, the results of the present investigation showed the existence of a single fixed point, as the only global attractor characterized by the equation N=pe(-qN) - μN.},
 year = {2021}
}

Copy | Download

TY  - JOUR
T1  - Study of the Existence of Global Attractors for the Wezewska, Czyewska and Lasota Models
AU  - Edgar Alí Medina
AU  - Manuel Vicente Centeno-Romero
AU  - Fernando José Marval López
AU  - José Feliciano Lockiby Aguirre
Y1  - 2021/08/31
PY  - 2021
N1  - https://doi.org/10.11648/j.ml.20210703.11
DO  - 10.11648/j.ml.20210703.11
T2  - Mathematics Letters
JF  - Mathematics Letters
JO  - Mathematics Letters
SP  - 37
EP  - 40
PB  - Science Publishing Group
SN  - 2575-5056
UR  - https://doi.org/10.11648/j.ml.20210703.11
AB  - In this research we present a study of global attractors in mathematical models of differential equations, which are an important tool in mathematics; furthermore, taking advantage of the stability of the solutions, it was possible to determine the control of biomedical phenomena, among other aspects, present in various population groups. Likewise, differential equation models are used to simulate biological, epidemiological and medical phenomena, among others. The reference population groups used in this research are the family of population models given by the differential equations N'(t)=p(t, N (t)) - d(t, N (t)). A particular case of this family of differential equations is the mathematical model called the Wezewska, Czyewska and Lasota (WCL) model, whose form is given by: N'(t)=pe(-q) - μN (t). This model describes the survival of red blood cells (erythrocytes) in humans. The WCL model, in discrete variable, has a non-trivial global attractor. In this research we demonstrate, using the Schwarz derivative technique, the existence of at least one model global attractor. On the other hand, the results of the present investigation showed the existence of a single fixed point, as the only global attractor characterized by the equation N=pe(-qN) - μN.
VL  - 7
IS  - 3
ER  -

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