CANARDS EXISTENCE IN THE HINDMARSH-ROSE MODEL

被引：5
|
作者：
Ginoux, Jean-Marc [1 ]
Llibre, Jaume [2 ]
Tchizawa, Kiyoyuki [3 ]
机构：
[1] Univ Toulon & Var, Lab Informat & Syst, UMR, CNRS 7020, BP 20132, F-83957 La Garde, France
[2] Univ Autonoma Barcelona, Dept Matemat, E-08193 Barcelona, Catalonia, Spain
[3] Inst Adm Engn Ltd, Tokyo 1010021, Japan
来源：
MATHEMATICAL MODELLING OF NATURAL PHENOMENA | 2019年 / 14卷 / 04期
基金：
欧盟地平线“2020”;
关键词：
Hindmarsh-Rose model; singularly perturbed dynamical systems; canard solutions; ASYMPTOTIC STABILITY; SYSTEMS;
D O I：
10.1051/mmnp/2019012
中图分类号：
Q [生物科学];
学科分类号：
07 ; 0710 ; 09 ;
摘要：
In two previous papers we have proposed a new method for proving the existence of "canard solutions" on one hand for three and four-dimensional singularly perturbed systems with only one fast variable and, on the other hand for four-dimensional singularly perturbed systems with two fast variables [J.M. Ginoux and J. Llibre, Qual. Theory Dyn. Syst. 15 (2016) 381-431; J.M. Ginoux and J. Llibre, Qual. Theory Dyn. Syst. 15 (2015) 342010]. The aim of this work is to extend this method which improves the classical ones used till now to the case of three-dimensional singularly perturbed systems with two fast variables. This method enables to state a unique generic condition for the existence of "canard solutions" for such three-dimensional singularly perturbed systems which is based on the stability of folded singularities (pseudo singular points in this case) of the normalized slow dynamics deduced from a well-known property of linear algebra. Applications of this method to a famous neuronal bursting model enables to show the existence of "canard solutions" in the Hindmarsh-Rose model.
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页数：21
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