The stability bounds of linear time-delay-singularly perturbed systems

2005 ◽  
Author(s):  
Z.H. Shao ◽  
J.R. Rowland
Keyword(s):  
Time Delay ◽  
Linear Time ◽  
Singularly Perturbed ◽  
Singularly Perturbed Systems ◽  
Perturbed Systems ◽  
The Stability

scholarly journals Stability bound analysis of singularly perturbed systems with time-delay

2013 ◽  
Vol 19 (4) ◽  
pp. 505-511 ◽  
Author(s):  
Fengqi Sun ◽  
Chunyu Yang ◽  
Qingling Zhang ◽  
Yongxiang Shen
Keyword(s):  
Time Delay ◽  
Singularly Perturbed ◽  
Stability Criteria ◽  
Singularly Perturbed Systems ◽  
Numerical Examples ◽  
Stability Bound ◽  
Perturbed Systems ◽  
The Stability ◽  
Bound Analysis

This paper considers the stability bound problem of singularly perturbed systems with time-delay. Some stability criteria are derived by constructing appropriate Lyapunov-Krasovskii functionals. The proposed criteria are less conservative than the existing ones. Two numerical examples are given to illustrate the advantages and effectiveness of the proposed methods.

scholarly journals Canards Existence in FitzHugh-Nagumo and Hodgkin-Huxley Neuronal Models

2015 ◽  
Vol 2015 ◽  
pp. 1-17 ◽  
Author(s):  
Jean-Marc Ginoux ◽  
Jaume Llibre
Keyword(s):  
Linear Algebra ◽  
Singular Points ◽  
Singularly Perturbed ◽  
New Method ◽  
Singularly Perturbed Systems ◽  
Slow Dynamics ◽  
Generic Condition ◽  
Perturbed Systems ◽  
Nagumo Equations ◽  
The Stability

In a previous paper we have proposed a new method for proving the existence of “canard solutions” for three- and four-dimensional singularly perturbed systems with only onefastvariable which improves the methods used until now. The aim of this work is to extend this method to the case of four-dimensional singularly perturbed systems with twoslowand twofastvariables. This method enables stating a unique generic condition for the existence of “canard solutions” for such four-dimensional singularly perturbed systems which is based on the stability offolded singularities(pseudo singular pointsin this case) of thenormalized slow dynamicsdeduced from a well-known property of linear algebra. This unique generic condition is identical to that provided in previous works. Application of this method to the famous coupled FitzHugh-Nagumo equations and to the Hodgkin-Huxley model enables showing the existence of “canard solutions” in such systems.

Sign in / Sign up

Export Citation Format

Share Document