Quantitative study of the regulatory mechanisms of cardiac activity and liver function in pathogenesis

Abstract

The article is devoted to investigate the dynamics of behavior of functional-differential equation with delay of mathematical model of the regulatory mechanisms of cardiac activity and liver function in pathogenesis. Moreover, the results of the computational experiment for the quantitative analysis of the object state are presented. The behavior of the system in the zone of dynamic chaos was analyzed with the use of developed software.

Mathematical Modeling of Vitiligo Origin and Development with Taking Into Account the Regulatory MicroRNAs

“…Computational experiments have shown that microRNAs are highly activated in the skin epidermis affected by vitiligo. The model results are in good agreement with experimental data [11]. The area of irregular fluctuations is characterized by regulatory system infraction with a consecutive impairment in skin functional activity.…”

Mathematical Modeling of Regulatory Mechanisms for the Propagation of Excitation in the Central Nervous System

“…Moreover, such a choice of coefficients significantly complicates the analysis of the system [6]. With application of functional differential equations with delayKhidirov, the modeled system has an innate tendency to the presence of an oscillatory mode of solutions [7][8][9][10][11]. Since these equations make it possible to take into account the temporal relationships in the regulation system, their use for modeling the regulatory mechanisms of the propagation of excitation in the CNS is most justified.…”

On Solving Biological Problem Based on Functional-Differential Equations of Delay Type With Discrete Experimental Data.

“…In mathematical modeling of the regulatory mechanisms of complex, interconnected systems, such as living systems, it is very important to choose a class of mathematical equations that have an "native" ability to oscillate modes of solutions, as well as suitable for modeling biosystems in normal conditions, anomalies, and when there is exist sudden activity death [1,2]. Such equations are functional differential equations with a delayed argument, constructed on the basis of the methods of regulating living systems [3,4]. Functional differential equations of regulatory mechanisms of biological systems are not integrated and obtaining exact solutions is generally impossible [1][2][3][4][5][6][7][8][9].…”

“…Such equations are functional differential equations with a delayed argument, constructed on the basis of the methods of regulating living systems [3,4]. Functional differential equations of regulatory mechanisms of biological systems are not integrated and obtaining exact solutions is generally impossible [1][2][3][4][5][6][7][8][9]. Using methods of qualitative analysis allows us to identify the general properties of solutions, to determine the characteristic stationary solutions and the existence of periodic solutions.…”