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.
Highlights
The study of global attractors in models of differential equations, as well as their existence, definition, stability and application in various spaces and models, has been treated in recent years by several researchers, as expressed in [1,2,3,4,5,6,7,8]
This article is motivated by works [1,2,3], where the authors study the existence of global attractors for equations in differences of the Wezewska, Czyewska and Lasota (WCL) model, on the existence of the fixed point
It should be noted that models such as those treated in the works mentioned above were described, for the first time, using differential equations, in [11, 12]
Summary
The study of global attractors in models of differential equations, as well as their existence, definition, stability and application in various spaces and models, has been treated in recent years by several researchers, as expressed in [1,2,3,4,5,6,7,8]. This article is motivated by works [1,2,3], where the authors study the existence of global attractors for equations in differences of the Wezewska, Czyewska and Lasota (WCL) model, on the existence of the fixed point. Edgar Alí Medina et al.: Study of the Existence of Global Attractors for the Wezewska, Czyewska and Lasota Models production rate of the cells at time t, provided that the population size is N and d(t, N(t)) is the rate of mortality. It was a common belief for researchers that mortality was proportional to the number of circulating blood cells; that is: d(t, N (t))=μN(t). To prove the existence of a single fixed point, as a single global attractor, characterized by equation (2)
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
