scholarly journals Exponential Decay for a System of Equations with Distributed Delays

2015 ◽  
Vol 2015 ◽  
pp. 1-6
Author(s):  
Nasser-Eddine Tatar
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Exponential Decay ◽  
Distributed Delay ◽  
Distributed Delays ◽  
System Of Equations ◽  
Activation Functions ◽  
Convergence Of Solutions

We prove convergence of solutions to zero in an exponential manner for a system of ordinary differential equations. The feature of this work is that it deals with nonlinear non-Lipschitz and unbounded distributed delay terms involving non-Lipschitz and unbounded activation functions.

scholarly journals Control of systems with Holder continuous functions in the distributed delays

2014 ◽  
Vol 30 (1) ◽  
pp. 123-128
Author(s):  
NASSER-EDDINE TATAR ◽  
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Continuous Functions ◽  
Distributed Delays ◽  
Exponential Stabilization ◽  
Activation Functions ◽  
Hölder Continuous ◽  
Lipschitz Continuous ◽  
Hölder Continuous Functions ◽  
Doubly Nonlinear

An exponential stabilization result is proved for a doubly nonlinear distributed delays system of ordinary differential equations. The problem involves non-Lipschitz continuous distributed delays of non-Lipschitz continuous ”activation” functions. This extends similar previous works where the distributed delays as well as the activation functions were assumed to be Lipschitz continuous.

scholarly journals On solvability of a nonlinear system of equations for the Fourier-Chebyshev coefficients in the problem of solving ordinary differential equations using Chebyshev series

2017 ◽  
pp. 169-174
Author(s):  
О.Б. Арушанян ◽  
С.Ф. Залеткин
Keyword(s):  
Nonlinear System ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Analytical Method ◽  
System Of Equations ◽  
Chebyshev Series ◽  
Nonlinear System Of Equations ◽  
Theoretical Substantiation ◽  
Solvability Theorem ◽  
Numerical Analytical Method

Сформулирована и доказана теорема о разрешимости нелинейной системы уравнений относительно приближенных значений коэффициентов Фурье-Чебышёва. Теорема является теоретическим обоснованием ранее предложенного численно-аналитического метода интегрирования обыкновенных дифференциальных уравнений с использованием рядов Чебышёва. A solvability theorem for a nonlinear system of equations with respect to approximate values of Fourier-Chebyshev coefficients is formulated and proved. This theorem is a theoretical substantiation for the previously proposed numerical-analytical method of solving ordinary differential equations using Chebyshev series.

On Axisymmetrical Deformations of Nonlinear Membranes

1970 ◽  
Vol 37 (4) ◽  
pp. 1002-1011 ◽  
Author(s):  
W. H. Yang ◽  
W. W. Feng
Keyword(s):  
Numerical Methods ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Elastic Stress ◽  
Material Behavior ◽  
System Of Equations ◽  
Initial Value ◽  
First Order ◽  
Stress Strain Relation ◽  
Flat Membrane

The mechanics problem concerning large axisymmetric deformations of nonlinear membranes is reformulated in terms of a system of three first-order ordinary differential equations with explicit derivatives. With a set of proper boundary conditions, arrangements are made to change the boundary-value problem into the form of an initial value problem such that the solution can be obtained by standard numerical methods for integrating ordinary differential equations. The system of equations derived applies to the class of all axisymmetric deformations of membranes with a general elastic stress-strain relation. Three examples are given on inflating of a flat membrane, longitudinal stretching of a tube, and flattening of a semispherical cap. In the examples, the Mooney model are assumed to describe the material behavior of the membranes. The solution on the flat membrane serves to compare with an existing one in literature. The solutions on the tube and the cap are new.

scholarly journals Logarithmic norms and regular perturbations of differential equations

2020 ◽  
Vol 73 (2) ◽  
pp. 5
Author(s):  
Jacek Banasiak
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Logarithmic Norm ◽  
Convergence Of Solutions ◽  
Logarithmic Norms ◽  
Perturbed Systems

In this note we explore the concept of the logarithmic norm of a matrix and illustrate its applicability by using it to find conditions under which the convergence of solutions of regularly perturbed systems of ordinary differential equations is uniform globally in time.

scholarly journals Asymptotic equivalence of ordinary and operator-differential equations

1987 ◽  
Vol 35 (3) ◽  
pp. 415-425 ◽  
Author(s):  
P. S. Simeonov ◽  
D. D. Bainov
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Distributed Delay ◽  
Asymptotic Equivalence ◽  
Specific Choice ◽  
System 2 ◽  
Image Position

The paper considers problems connected with the asymptotic equivalence of the system of ordinary differential equationsand the system of operator differential equationsThe generality of the operator At guarantees a number of its important implementations. By a specific choice of the operator At the system (2) can be one of the concentrated delay, a system of distributed delay, a system with maxima, etcetera.

scholarly journals Qualitative Analysis of a Single-Species Model with Distributed Delay and Nonlinear Harvest

Mathematics ◽  
2021 ◽  
Vol 9 (20) ◽  
pp. 2560
Author(s):  
Zuxiong Li ◽  
Shengnan Fu ◽  
Huili Xiang ◽  
Hailing Wang
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Sufficient Conditions ◽  
Distributed Delay ◽  
Single Species ◽  
Dimensional System ◽  
Globally Asymptotically Stable ◽  
Species Population ◽  
Existence And Stability ◽  
Single Species Population

In this paper, a single-species population model with distributed delay and Michaelis-Menten type harvesting is established. Through an appropriate transformation, the mathematical model is converted into a two-dimensional system. Applying qualitative theory of ordinary differential equations, we obtain sufficient conditions for the stability of the equilibria of this system under three cases. The equilibrium A1 of system is globally asymptotically stable when br−c>0 and η<0. Using Poincare-Bendixson theorem, we determine the existence and stability of limit cycle when br−c>0 and η>0. By computing Lyapunov number, we obtain that a supercritical Hopf bifurcation occurs when η passes through 0. High order singularity of the system, such as saddle node, degenerate critical point, unstable node, saddle point, etc, is studied by the theory of ordinary differential equations. Numerical simulations are provided to verify our main results in this paper.

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