Oscillations in Low-Dimensional Cyclic Differential Delay Systems

2018 ◽  
pp. 603-613
Author(s):  
Anatoli F. Ivanov ◽  
Zari A. Dzalilov
Keyword(s):  
Delay Systems ◽  
Differential Delay ◽  
Low Dimensional

On linear generalized neutral differential delay systems

2009 ◽  
Vol 346 (7) ◽  
pp. 691-704 ◽  
Author(s):  
Athanasios A. Pantelous ◽  
Grigoris I. Kalogeropoulos
Keyword(s):  
Delay Systems ◽  
Differential Delay

scholarly journals On the Number of Periodic Orbits to Odd Order Differential Delay Systems

Mathematics ◽  
2020 ◽  
Vol 8 (10) ◽  
pp. 1731
Author(s):  
Weigao Ge ◽  
Lin Li
Keyword(s):  
Variational Method ◽  
Periodic Orbits ◽  
Index Theory ◽  
Accurate Method ◽  
Delay System ◽  
Delay Systems ◽  
Differential Delay ◽  
Odd Order

In this paper, we study the periodic orbits of a type of odd order differential delay system with 2k−1 lags via the S1 index theory and the variational method. This type of system has not been studied by others. Our results provide a new and more accurate method for counting the number of periodic orbits.

Statistics and dimension of chaos in differential delay systems

1987 ◽  
Vol 35 (1) ◽  
pp. 328-339 ◽  
Author(s):  
B. Dorizzi ◽  
B. Grammaticos ◽  
M. Le Berre ◽  
Y. Pomeau ◽  
E. Ressayre ◽  
...  
Keyword(s):  
Delay Systems ◽  
Differential Delay

Discretized Lyapunov-Krasovskii Functional for Systems With Multiple Delay Channels

2008 ◽  
Author(s):  
Hongfei Li ◽  
Keqin Gu
Keyword(s):  
Time Delay ◽  
Standard Form ◽  
Computational Effort ◽  
Delay Systems ◽  
Linear Matrix ◽  
Time Delay Systems ◽  
State Variables ◽  
Regular Time ◽  
Low Dimensional ◽  
Necessary And Sufficient

Many practical systems have a large number of state variables but only a few components have time delays. These delay components are often scalar or low dimensional, and involve single time delay in each component. A coupled differential-difference equation is well suited to formulate such systems. It is known that such a formulation is very general. Systems with multiple related or independent delays can be transformed into this standard form. Similar to regular time-delay systems, the existence of a quadratic Lyapunov-Krasovkii functional is necessary and sufficient for stability. This article discusses the discretization of such a quadratic Lyapunov-Krasovskii functional. Even for time-delay systems of retarded type, the formulation has significant advantage over the traditional formulation, as the size of the resulting linear matrix inequalities are drastically reduced for such systems. Indeed, the computational effort needed for checking stability of such a large system with a few low dimensional delays is quite reasonable.

Exponential stability of stochastic differential delay systems with delayed impulse effects

2011 ◽  
Vol 52 (9) ◽  
pp. 092702 ◽  
Author(s):  
Xiaotai Wu ◽  
Litan Yan ◽  
Wenbing Zhang ◽  
Yang Tang
Keyword(s):  
Exponential Stability ◽  
Delay Systems ◽  
Differential Delay ◽  
Delayed Impulse

Inverse differential-delay systems

1974 ◽  
Vol 19 (1) ◽  
pp. 87-88 ◽  
Author(s):  
G. Nazaroff
Keyword(s):  
Delay Systems ◽  
Differential Delay

Stability of nonlinear differential delay systems

1998 ◽  
Vol 45 (3-4) ◽  
pp. 257-267 ◽  
Author(s):  
Erik I. Verriest ◽  
Woihida Aggoune
Keyword(s):  
Delay Systems ◽  
Differential Delay

Stability of linear stochastic differential delay systems under impulsive control

2009 ◽  
Vol 3 (11) ◽  
pp. 1547-1552 ◽  
Author(s):  
S.W. Zhao ◽  
J.T. Sun ◽  
H.J. Wu
Keyword(s):  
Impulsive Control ◽  
Delay Systems ◽  
Differential Delay
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