scholarly journals BEHAVIOR OF THE PHARMACOKINETICS OF ENROFLOXACIN IN THE PHASE SPACE

2019 ◽  
Vol 7 (4) ◽  
pp. 288-293
Author(s):  
Miroslav Vasilev ◽  
Galya Shivacheva
Keyword(s):  
Comparative Analysis ◽  
Plasma Concentration ◽  
Phase Space ◽  
Differential Equations ◽  
Mathematical Models ◽  
Blood Plasma ◽  
Graphical Representation ◽  
Nonlinear Differential Equations ◽  
Qualitative Assessment ◽  
Second Order Differential Equations

Phase space is an approach for analysis of nonlinear differential equations. The graphical solutions that are obtained are convenient for qualitative assessment of the behavior of systems and processes. A comparative analysis of the pharmacokinetics of the antibiotic enrofloxacin administered intravenously in dogs and cats has been performed in the present study. The mathematical models that represent the change in blood plasma concentration of the two groups of animals are described by second-order differential equations. For the graphical representation of phase trajectories using the fluoroquinolone, the Mathcad program tools are used. The properties of the peculiar points are determined based on the received images.

BEHAVIOR OF THE PHARMACOKINETICS OF ENROFLOXACIN IN THE PHASE SPACE

2019 ◽  
pp. 77-83
Author(s):  
Miroslav Vasilev ◽  
Galya Shivacheva
Keyword(s):  
Comparative Analysis ◽  
Plasma Concentration ◽  
Phase Space ◽  
Differential Equations ◽  
Mathematical Models ◽  
Blood Plasma ◽  
Graphical Representation ◽  
Nonlinear Differential Equations ◽  
Qualitative Assessment ◽  
Second Order Differential Equations

Phase space is an approach for analysis of nonlinear differential equations. The graphical solutions that are obtained are convenient for qualitative assessment of the behavior of systems and processes. A comparative analysis of the pharmacokinetics of the antibiotic enrofloxacin administered intravenously in dogs and cats has been performed in the present study. The mathematical models that represent the change in blood plasma concentration of the two groups of animals are described by second-order differential equations. For the graphical representation of phase trajectories using the fluoroquinolone, the Mathcad program tools are used. The properties of the peculiar points are determined based on the received images.

scholarly journals Existence and Multiplicity Results for Nonlinear Differential Equations Depending on a Parameter in Semipositone Case

2012 ◽  
Vol 2012 ◽  
pp. 1-10 ◽  
Author(s):  
Hailong Zhu ◽  
Shengjun Li
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Nonlinear Differential Equations ◽  
Multiplicity Results ◽  
Second Order Differential Equations ◽  
Existence And Multiplicity ◽  
Nonlinear Alternative ◽  
Krasnosel’Skii’S Fixed Point Theorem ◽  
Alternative Principle

The existence and multiplicity of solutions for second-order differential equations with a parameter are discussed in this paper. We are mainly concerned with the semipositone case. The analysis relies on the nonlinear alternative principle of Leray-Schauder and Krasnosel'skii's fixed point theorem in cones.

scholarly journals Integrability via Functional Expansion for the KMN Model

Symmetry ◽  
2020 ◽  
Vol 12 (11) ◽  
pp. 1819
Author(s):  
Radu Constantinescu ◽  
Aurelia Florian
Keyword(s):  
Differential Equations ◽  
Traveling Wave ◽  
Nonlinear Differential Equations ◽  
Traveling Wave Solutions ◽  
Auxiliary Equation ◽  
First Order ◽  
Second Order Differential Equations ◽  
Functional Expansion ◽  
Wave Solutions ◽  
First Time

This paper considers issues such as integrability and how to get specific classes of solutions for nonlinear differential equations. The nonlinear Kundu–Mukherjee–Naskar (KMN) equation is chosen as a model, and its traveling wave solutions are investigated by using a direct solving method. It is a quite recent proposed approach called the functional expansion and it is based on the use of auxiliary equations. The main objectives are to provide arguments that the functional expansion offers more general solutions, and to point out how these solutions depend on the choice of the auxiliary equation. To see that, two different equations are considered, one first order and one second order differential equations. A large variety of KMN solutions are generated, part of them listed for the first time. Comments and remarks on the dependence of these solutions on the solving method and on form of the auxiliary equation, are included.

Research and Analysis of Dynamic Behaviour in the Mathematical Models of the 6-Axle Locomotive

2011 ◽  
Vol 105-107 ◽  
pp. 541-544
Author(s):  
Van Tham Mai ◽  
Shi Jing Wu ◽  
Xiao Sun Wang ◽  
Jie Chen ◽  
S. A. K. S. Jafri
Keyword(s):  
Differential Equations ◽  
Mathematical Models ◽  
Dynamic Behavior ◽  
Dynamic Behaviour ◽  
Computer Software ◽  
Rolling Contact ◽  
Rolling Stock ◽  
Vertical Movements ◽  
Dynamic Behaviors ◽  
Second Order Differential Equations

With the aiming of mathematically modeling dynamic behavior in latitudinal and vertical movements of the 6-axle locomotive, this paper introduces the Kalker’s Wheel-Rail Rolling Contact Theories and their implementation in multibody codes. This paper also highlights methodology for solving inhomogeneous linear second-order differential equations with MATLAB computer software aided. The calculation has reported that the dynamic behaviors of Diesel-Electric 6-axle locomotive are significantly demonstrated. The calculation has reported that the dynamic behaviors of Diesel-Electric 6-axle locomotive are significantly demonstrated the requirements on Rolling stock Dynamic behaviors of Vietnam Railways.

scholarly journals Existence, uniqueness, and quasilinearization results for nonlinear differential equations arising in viscoelastic fluid flow

2006 ◽  
Vol 2006 ◽  
pp. 1-9 ◽  
Author(s):  
F. Talay Akyildiz ◽  
K. Vajravelu
Keyword(s):  
Fluid Flow ◽  
Differential Equations ◽  
Viscoelastic Fluid ◽  
Poiseuille Flow ◽  
Nonlinear Differential Equations ◽  
Second Order ◽  
Numerical Results ◽  
Second Order Differential Equations ◽  
Salient Features ◽  
Quasilinearization Technique

Solutions for a class of nonlinear second-order differential equations arising in steady Poiseuille flow of an Oldroyd six-constant model are obtained using the quasilinearization technique. Existence, uniqueness, and analyticity results are established using Schauder theory. Numerical results are presented graphically and salient features of the solutions are discussed.

Oscillation of second-order nonlinear differential equations with damping

2014 ◽  
Vol 64 (5) ◽  
Author(s):  
Tongxing Li ◽  
Yuriy Rogovchenko ◽  
Shuhong Tang
Keyword(s):  
Differential Equations ◽  
Nonlinear Differential Equations ◽  
Nonlinear Damping ◽  
Second Order ◽  
Oscillation Criteria ◽  
Second Order Differential Equations ◽  
Nonlinear Anal ◽  
Oscillatory Properties

AbstractWe study oscillatory properties of solutions to a class of nonlinear second-order differential equations with a nonlinear damping. New oscillation criteria extend those reported in [ROGOVCHENKO, Yu. V.—TUNCAY, F.: Oscillation criteria for second-order nonlinear differential equations with damping, Nonlinear Anal. 69 (2008), 208–221] and improve a number of related results.

Stability of an Axial Flow Compressor with Steady Inlet Conditions

1974 ◽  
Vol 16 (6) ◽  
pp. 377-385 ◽  
Author(s):  
A. G. Corbett ◽  
R. L. Elder
Keyword(s):  
Differential Equations ◽  
Mathematical Models ◽  
Dynamic Behaviour ◽  
Nonlinear Differential Equations ◽  
Axial Flow ◽  
Axial Flow Compressor ◽  
Inlet Conditions ◽  
Flow Compressor

A series of mathematical models of varying complexity which describe the dynamic behaviour of an axial flow compressor as a set of nonlinear differential equations are derived in a systematic way. These models are justified by comparing their stability with experimental surge data.

scholarly journals ANALYSIS OF FORCED VIBRATIONS OF NONLINEAR PLATES IN A VISCOELASTIC MEDIUM UNDER THE CONDITIONS OF THE DIFFERENT COMBINATIONAL INTERNAL

2019 ◽  
Vol 15 (3) ◽  
pp. 131-148
Author(s):  
Marina Shitikova ◽  
Vladimir Kandu
Keyword(s):  
Comparative Analysis ◽  
Differential Equations ◽  
Dynamic Response ◽  
Fractional Derivative ◽  
Viscoelastic Medium ◽  
Nonlinear Differential Equations ◽  
Forced Vibrations ◽  
Numerical Calculations ◽  
Free And Forced Vibrations ◽  
Nonlinear Plate

In the present paper, the force driven dynamic response of a nonlinear plate embedded in a viscoelastic medium, damping features of which are described by the Kelvin-Voigt fractional derivative model, is studied. The motion of the plate is described by three coupled nonlinear differential equations with due account for the fact that the plate is being under the conditions of the internal combinational resonance accompanied by the external resonance, resulting in the interaction of three modes corresponding to the mutually orthogonal displacements. A comparative analysis of numerical calculations for the cases of free and forced vibrations has been carried out.

scholarly journals Dynamics of the mathematical model of phase-locked systems with delay

2021 ◽  
Vol 23 (1) ◽  
pp. 28-42
Author(s):  
Sergei S. Mamonov ◽  
Irina V. Ionova ◽  
Anastasiya O. Kharlamova
Keyword(s):  
Mathematical Model ◽  
Comparative Analysis ◽  
Differential Equations ◽  
Limit Cycles ◽  
Second Order ◽  
Second Order Differential Equations ◽  
Self Tuning ◽  
Phase Systems ◽  
Tuning Systems ◽  
The Mathematical Model

In the article, the conditions for the existence of limit cycles of the first kind are obtained for self-tuning systems with delay, which, in turn, determine the conditions for the occurrence of hidden synchronization modes in such systems. The principle of the proof is based on constructing a positively invariant toroidal set using two cylindrical surfaces, whose boundaries are determined by the limit cycles of a system of the second-order differential equations. Using the results obtained in the article for limit cycles, the possibility of using the curvature of the cycle for a comparative analysis of the proximity of the cycles of phase and non-phase systems, as well as for determining the mode of hidden synchronization, is shown.

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