On the asymptotic integration of a singularly perturbed system of linear differential equations with deviating argument

2010 ◽  
Vol 13 (2) ◽  
pp. 178-195
Author(s):  
I. H. Klyuchnyk ◽  
H. V. Zavizion
Keyword(s):  
Differential Equations ◽  
Linear Differential Equations ◽  
Singularly Perturbed ◽  
Asymptotic Integration ◽  
Singularly Perturbed System ◽  
Deviating Argument ◽  
Perturbed System ◽  
Linear Differential

scholarly journals Boundary value problem for a singularly perturbed system of linear differential equations with impulses

1988 ◽  
Vol 31 (1) ◽  
pp. 107-126 ◽  
Author(s):  
D. D. Bainov ◽  
M. A. Hekimova ◽  
V. M. Veliov
Keyword(s):  
Differential Equations ◽  
Boundary Value Problem ◽  
Mathematical Models ◽  
Automatic Control ◽  
Linear Differential Equations ◽  
Singularly Perturbed ◽  
Singularly Perturbed System ◽  
Perturbed System ◽  
Linear Differential ◽  
Short Time

In connection with the analysis of mathematical models of real processes undergoing short time perturbations, in the last years the interest in the differential equations with impulses remarkably increased. Going back to the papers of Mil'man and Myshkis [4, 5] the investigations of this subject are now extended to different directions concerning applications in physics, biology, electronics, automatic control etc.

NUMERICAL COMPUTATION OF CANARDS

2000 ◽  
Vol 10 (12) ◽  
pp. 2669-2687 ◽  
Author(s):  
JOHN GUCKENHEIMER ◽  
KATHLEEN HOFFMAN ◽  
WARREN WECKESSER
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Electrical Potential ◽  
Slow Manifold ◽  
Singularly Perturbed ◽  
Singularly Perturbed Systems ◽  
Singularly Perturbed System ◽  
Chemical Systems ◽  
Perturbed System ◽  
Physical And Chemical

Singularly perturbed systems of ordinary differential equations arise in many biological, physical and chemical systems. We present an example of a singularly perturbed system of ordinary differential equations that arises as a model of the electrical potential across the cell membrane of a neuron. We describe two periodic solutions of this example that were numerically computed using continuation of solutions of boundary value problems. One of these periodic orbits contains canards, trajectory segments that follow unstable portions of a slow manifold. We identify several mechanisms that lead to the formation of these and other canards in this example.

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