scholarly journals BEYOND SLOW-FAST: RELAXATION OSCILLATIONS IN SINGULARLY PERTURBED NONSMOOTH SYSTEMS

2021 ◽  
pp. 1-2
Author(s):  
SAMUEL JELBART
Keyword(s):  
Singularly Perturbed ◽  
Relaxation Oscillations ◽  
Nonsmooth Systems ◽  
Fast Relaxation

scholarly journals RELAXATION OSCILLATIONS IN SINGULARLY PERTURBED GENERALIZED LIENARD SYSTEMS WITH NON-GENERIC TURNING POINTS

2017 ◽  
Vol 22 (3) ◽  
pp. 389-407 ◽  
Author(s):  
Huan Hu ◽  
Jianhe Shen ◽  
Zheyan Zhou ◽  
Zhonghui Ou
Keyword(s):  
Turning Point ◽  
Singularly Perturbed ◽  
Relaxation Oscillations ◽  
Biological Models ◽  
Asymptotic Behaviors ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Liénard Systems ◽  
Analysis Technique ◽  
Specific Parameter

Based on the asymptotic analysis technique developed by Eckhaus [Lecture Notes in Math., vol. 985, pp 449-494. Springer, Berlin, 1983], this paper aims to study the existence and the asymptotic behaviors of relaxation oscillations of regular and canard types in a singularly perturbed generalized Lionard system with a non-generic turning point. The singularly perturbed Lionard system considered in this paper is very general and numerous real world models like some biological ones can be rewritten in the form of this system after a series of transformations. Under certain conditions, we rigorously prove the existence of regular relaxation oscillations and canard relaxation oscillations under the specific parameter conditions. As an application, two biological models, namely, a FitzHugh-Nagumo model and a twodimensional predator-prey model with Holling-II response are studied, in which, the existence of regular relaxation oscillations and canard relaxation oscillations as well as the bifurcation curves are obtained.

The theory of nonclassical relaxation oscillations in singularly perturbed delay systems

2014 ◽  
Vol 205 (6) ◽  
pp. 781-842 ◽  
Author(s):  
S. D. Glyzin ◽  
A. Yu. Kolesov ◽  
N. Kh. Rozov
Keyword(s):  
Singularly Perturbed ◽  
Delay Systems ◽  
Relaxation Oscillations

A remark on stabilization of nonsmooth systems

1999 ◽  
Author(s):  
W. Aggoime ◽  
Rm Outbib ◽  
M. Darouach
Keyword(s):  
Nonsmooth Systems

Regularization of Integral Operators in Singularly Perturbed Problems Using Normal Forms

Vestnik MEI ◽  
2019 ◽  
Vol 6 ◽  
pp. 131-137
Author(s):  
Abdukhafiz A. Bobodzhanova ◽  
◽  
Valeriy F. Safonov ◽  
Keyword(s):  
Normal Forms ◽  
Integral Operators ◽  
Singularly Perturbed ◽  
Singularly Perturbed Problems
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