On the stability of coupled delay differential and continuous time difference equations

2004 ◽  
Author(s):  
P. Pepe ◽  
E.I. Verriest
Keyword(s):  
Difference Equations ◽  
Continuous Time ◽  
Time Difference ◽  
The Stability ◽  
Delay Differential

Exponential L2-stability for a class of linear systems governed by continuous-time difference equations

Automatica ◽  
2014 ◽  
Vol 50 (12) ◽  
pp. 3299-3303 ◽  
Author(s):  
Sérine Damak ◽  
Michael Di Loreto ◽  
Warody Lombardi ◽  
Vincent Andrieu
Keyword(s):  
Linear Systems ◽  
Difference Equations ◽  
Continuous Time ◽  
Time Difference

The Magnus Expansion for Periodic Delay Differential Equations

2013 ◽  
Author(s):  
Árpád Takács ◽  
Eric A. Butcher ◽  
Tamás Insperger
Keyword(s):  
Differential Equations ◽  
Continuous Time ◽  
Delay Differential Equations ◽  
Approximation Technique ◽  
Magnus Expansion ◽  
Time Approximation ◽  
Delayed Differential Equations ◽  
Periodic Delay ◽  
The Stability ◽  
Delay Differential

In this paper, the application of the Magnus expansion on periodic time-delayed differential equations is proposed, where an approximation technique of Chebyshev Spectral Continuous Time Approximation (CSCTA) is first used to convert a system of delayed differential equations (DDEs) into a system of ordinary differential equations (ODEs), whose solution are then obtained via the Magnus expansion. The stability and time response of this approach are investigated on two examples and compared with known results in the literature.

scholarly journals Bifurcation Analysis of a Duopoly Game with R&D Spillover, Price Competition and Time Delays

Symmetry ◽  
2020 ◽  
Vol 12 (2) ◽  
pp. 257 ◽  
Author(s):  
B. A. Pansera ◽  
L. Guerrini ◽  
M. Ferrara ◽  
T. Ciano
Keyword(s):  
Continuous Time ◽  
Delay Differential Equations ◽  
Price Competition ◽  
Time Delays ◽  
Equilibrium Points ◽  
Hopf Bifurcations ◽  
Stage Game ◽  
Set Up ◽  
The Stability ◽  
Delay Differential

The aim of this study is to analyse a discrete-time two-stage game with R&D competition by considering a continuous-time set-up with fixed delays. The model is represented in the form of delay differential equations. The stability of all the equilibrium points is studied. It is found that the model exhibits very complex dynamical behaviours, and its Nash equilibrium is destabilised via Hopf bifurcations.

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