scholarly journals Asymptotic properties of an unstable two-dimensional differential system with delay

2006 ◽  
Vol 131 (3) ◽  
pp. 305-319
Author(s):  
Josef Kalas
Keyword(s):  
Differential System ◽  
Asymptotic Properties ◽  
Two Dimensional ◽  
System With Delay

scholarly journals Stability of a Functional Differential System with a Finite Number of Delays

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Josef Rebenda ◽  
Zdeněk Šmarda
Keyword(s):  
Asymptotic Stability ◽  
Differential System ◽  
Asymptotic Properties ◽  
Sufficient Conditions ◽  
Two Dimensional ◽  
Stability Of Solutions ◽  
Functional Differential ◽  
The Stability ◽  
Complex Valued ◽  
Functional Differential System

The paper is devoted to the study of asymptotic properties of a real two-dimensional differential system with unbounded nonconstant delays. The sufficient conditions for the stability and asymptotic stability of solutions are given. Used methods are based on the transformation of the considered real system to one equation with complex-valued coefficients. Asymptotic properties are studied by means of Lyapunov-Krasovskii functional. The results generalize some previous ones, where the asymptotic properties for two-dimensional systems with one or more constant delays or one nonconstant delay were studied.

Asymptotic behaviour of real two-dimensional differential system with a finite number of constant delays

2008 ◽  
Vol 41 (4) ◽  
Author(s):  
Josef Rebenda
Keyword(s):  
Finite Number ◽  
Asymptotic Behaviour ◽  
Differential System ◽  
Asymptotic Properties ◽  
Dimensional System ◽  
Two Dimensional ◽  
Two Dimensional System

AbstractIn this article stability and asymptotic properties of a real two-dimensional system

scholarly journals Asymptotic Behaviour of a Two-Dimensional Differential System with a Finite Number of Nonconstant Delays under the Conditions of Instability

2012 ◽  
Vol 2012 ◽  
pp. 1-20
Author(s):  
Zdeněk Šmarda ◽  
Josef Rebenda
Keyword(s):  
Finite Number ◽  
Asymptotic Behaviour ◽  
Vector Function ◽  
Differential System ◽  
Asymptotic Properties ◽  
Matrix Functions ◽  
Two Dimensional ◽  
Bounded Solutions ◽  
Complex Valued ◽  
Topological Principle

The asymptotic behaviour of a real two-dimensional differential system with unbounded nonconstant delays satisfying is studied under the assumption of instability. Here, , and are supposed to be matrix functions and a vector function. The conditions for the instable properties of solutions and the conditions for the existence of bounded solutions are given. The methods are based on the transformation of the considered real system to one equation with complex-valued coefficients. Asymptotic properties are studied by means of a Lyapunov-Krasovskii functional and the suitable Ważewski topological principle. The results generalize some previous ones, where the asymptotic properties for two-dimensional systems with one constant or nonconstant delay were studied.

scholarly journals Continuation and uniqueness for generalised Emden-Fowler systems

1991 ◽  
Vol 33 (1) ◽  
pp. 85-93 ◽  
Author(s):  
Lynn H. Erbe ◽  
Zhongchao Liang
Keyword(s):  
Cauchy Problem ◽  
Differential System ◽  
Two Dimensional ◽  
The Cauchy Problem

AbstractWe discuss uniqueness and continuation of solutions to the Cauchy problem for a two dimensional Emden-Fowler differential system.

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