Nonoccurence of Stability Switching in Systems with Discrete Delays

1988 ◽  
Vol 31 (1) ◽  
pp. 52-58 ◽  
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.

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

2017 ◽  
Vol 23 (2) ◽  
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

On non-oscillation for certain system of non-linear ordinary differential equations

2017 ◽  
Vol 24 (2) ◽  
pp. 277-285 ◽  
Author(s):  
Zdeněk Opluštil
Keyword(s):  
Differential Equations ◽  
Linear Equations ◽  
Dimensional System ◽  
Two Dimensional ◽  
Linear Ordinary Differential Equations ◽  
Second Order Differential Equations ◽  
Integrable Functions ◽  
Non Linear ◽  
Two Dimensional System ◽  
Non Linear Equations

AbstractWe consider the following two-dimensional system of non-linear equations:u^{\prime}=g(t)|v|^{\frac{1}{\alpha}}\operatorname{sgn}v,\quad v^{\prime}=-p(t% )|u|^{\alpha}\operatorname{sgn}u,where {\alpha>0}, and {g\colon{[0,+\infty[}\rightarrow{[0,+\infty[}} and {p\colon{[0,+\infty[}\rightarrow\mathbb{R}} are locally integrable functions. Moreover, we assume that the coefficient g is non-integrable on {[0,+\infty]}. We establish new non-oscillation criteria for the considered system, which generalize known results for the corresponding linear system and for second order differential equations. In particular, the presented criteria are in compliance with the results of Hille and Nehari.

Qualitative Investigation of Two-Dimensional Chua's System

2000 ◽  
Vol 7 (1) ◽  
pp. 191-200
Author(s):  
Sergiy Yanchuk
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Piecewise Linear ◽  
Qualitative Behavior ◽  
Dimensional System ◽  
Two Dimensional ◽  
Qualitative Investigation ◽  
Two Dimensional System ◽  
Parameter Values

Abstract The piecewise linear canonical Chua's system of ordinary differential equations is investigated. We consider the case when this problem can be reduced to a two-dimensional system with three parameters. For the reduced system, the qualitative behavior of solutions is analyzed for all parameter values. In particular, we indicate the parameters for which at least one, two or three nontrivial cycles exist.

Parallel navigation for reaching a moving goal by a mobile robot

Robotica ◽  
2006 ◽  
Vol 25 (1) ◽  
pp. 63-74 ◽  
Author(s):  
F. Belkhouche ◽  
B. Belkhouche ◽  
P. Rastgoufard
Keyword(s):  
Robot Navigation ◽  
Polar Coordinates ◽  
Control Law ◽  
Dimensional System ◽  
Two Dimensional ◽  
System Of Differential Equations ◽  
Extensive Simulation ◽  
Navigation Strategy ◽  
Two Dimensional System ◽  
Theoretical Results

In this paper, we present a method for robot navigation toward a moving object with unknown maneuvers. Our strategy is based on the integration of the robot and the target kinematics equations with geometric rules. The tracking problem is modeled in polar coordinates using a two-dimensional system of differential equations. The control law is then derived based on this model. Our approach consists of a rendezvous course, which means that the robot reaches the moving goal without following its path. In the presence of obstacles, two navigation modes are integrated, namely the tracking and the obstacle-avoidance modes. To confirm our theoretical results, the navigation strategy is illustrated using an extensive simulation for different scenarios.

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

Effect of partial ordering of a two-dimensional system of scatterers on the anisotropy of its kinetic coefficients

1998 ◽  
Vol 32 (10) ◽  
pp. 1116-1118
Author(s):  
N. S. Averkiev ◽  
A. M. Monakhov ◽  
A. Yu. Shik ◽  
P. M. Koenraad
Keyword(s):  
Partial Ordering ◽  
Dimensional System ◽  
Two Dimensional ◽  
Kinetic Coefficients ◽  
Two Dimensional System
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