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

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.

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ASYMPTOTIC BEHAVIOUR OF REAL TWO-DIMENSIONAL DIFFERENTIAL SYSTEM WITH A FINITE NUMBER OF CONSTANT DELAYS

Demonstratio Mathematica ◽

10.1515/dema-2008-0412 ◽

2008 ◽

Vol 41 (4) ◽

Author(s):

Josef Rebenda

Keyword(s):

Finite Number ◽

Asymptotic Behaviour ◽

Differential System ◽

Two Dimensional

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On the stability of steady-states of a two-dimensional system of ferromagnetic nanowires

Journal of Applied Analysis ◽

10.1515/jaa-2017-0013 ◽

2017 ◽

Vol 23 (2) ◽

Cited By ~ 6

Author(s):

Sharad Dwivedi ◽

Shruti Dubey

Keyword(s):

Finite Number ◽

Steady States ◽

Dimensional System ◽

Two Dimensional ◽

Ferromagnetic Nanowires ◽

Two Dimensional System ◽

The Stability

AbstractWe investigate the stability features of steady-states of a two-dimensional system of ferromagnetic nanowires. We constitute a system with the finite number of nanowires arranged on the

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MULTIPLE SOLUTIONS OF THE BVB FOR TWO‐DIMENSIONAL SYSTEM BY EXTRACTING LINEAR PARTS AND QUASILINEARIZATIO

Mathematical Modelling and Analysis ◽

10.3846/1392-6292.2008.13.303-312 ◽

2008 ◽

Vol 13 (2) ◽

pp. 303-312

Author(s):

Inara Yermachenko

Keyword(s):

Boundary Conditions ◽

Differential System ◽

Multiple Solutions ◽

Dimensional System ◽

Two Dimensional ◽

Two Dimensional System

We investigate a two-dimensional differential system of the form x' = f(t, y), y' = h(t, x) together with the boundary conditions x(0) = 0, x(1) = 0 by using the quasilinearization process. We show that if this problem allows for quasilinearization with respect to essentially different linear parts, then it has multiple solutions.

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Nonoccurence of Stability Switching in Systems with Discrete Delays

Canadian Mathematical Bulletin ◽

10.4153/cmb-1988-008-0 ◽

1988 ◽

Vol 31 (1) ◽

pp. 52-58 ◽

Cited By ~ 13

Author(s):

H. I. Freedman ◽

K. Gopalsamy

Keyword(s):

Differential Equations ◽

Finite Number ◽

Dimensional System ◽

Two Dimensional ◽

System Of Differential Equations ◽

Discrete Delays ◽

Two Dimensional System

AbstractA two dimensional system of differential equations with a finite number of discrete delays is considered. Conditions are derived for there to be no stability switching for arbitrary such delays.

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