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
Issue:
Volume 7, Issue 3, September 2021
Pages:
37-40
Received:
8 May 2021
Accepted:
21 July 2021
Published:
31 August 2021
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.
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,...
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Embedding Integral of a Linear Equation of Degree 3 with One Variable
Rena Eldar Kizi Kerbalayeva
Issue:
Volume 7, Issue 3, September 2021
Pages:
41-44
Received:
14 June 2021
Accepted:
6 September 2021
Published:
30 October 2021
Abstract: What should you able to see this paper? You will see some of calculation estimates and approximations that mathematics can perform as they solve technical problems and communicate their results. The origin of the Linear equation goes back to the early period of development of Mathematics and it is related to the method exhaustion developed by the mathematicians of ancient Babylon and Greece. In this sense, the method of the exhaustion can be regarded as an early method of calculus. The greatest development of method solution of such equation in the early period was obtained in the works Scipione dell Ferro and Niccolo Tartaglia (1539). Systematic approach to the theory of the Linear equation of degree three began in the 16th century. In this paper I studied some properties of the liner equation of degree 3. The concept of solutions of linear equations is one of most important mathematical concepts. I introduce embedding intervals of the linear equation of degree 3 with one variable. How many solutions are there to the equation? First and foremost, one can discover the definition of a linear equation of degree 3. The Fundamental theorem of Arithmetic says that, the solution of given equation is between divisors of constant term: leading coefficient. But it is very difficult to choose it among them. That is why, we need following condition. Second one can find condition for such equation. The idea that the solution of simultaneous equations y=x2, y=(–cx–d):(ax+b) is where the graphs intersect can be used too different situations. Your sketching determine the number of real roots of this equation. The solution to this equation are represented by the points where the graphs intersect. Then we can get y=±(–cx–d) and y=±(–cx-d)1/2×(ax+b)1/2. Consider such inequality one can solve by graphical method and by other methods, where c, b, c, d are real numbers, in addition, a≠–b:d. Here the expression (–cx–d):(ax+b) must be nonnegative. Using it we can find main condition for our given equation. Third I have placed several examples for improved pedagogical format compising the problem’s proof, solutions and discussion.
Abstract: What should you able to see this paper? You will see some of calculation estimates and approximations that mathematics can perform as they solve technical problems and communicate their results. The origin of the Linear equation goes back to the early period of development of Mathematics and it is related to the method exhaustion developed by the m...
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