A method for detecting false bifurcations in dynamical systems: application to neural-field models

被引：9

作者：

Rodrigues, Serafim ^{[1
]}

Barton, David ^{[1
]}

Marten, Frank ^{[1
]}

Kibuuka, Moses ^{[1
,2
]}

Alarcon, Gonzalo ^{[1
,2
]}

Richardson, Mark P. ^{[1
,2
]}

Terry, John R. ^{[1
]}

机构：

[1] Univ Bristol, Dept Engn Math, Bristol BS8 1TR, Avon, England

[2] Kings Coll London, Inst Psychiat, London SE5 8AF, England

来源：

BIOLOGICAL CYBERNETICS | 2010年 / 102卷 / 02期

基金：

英国工程与自然科学研究理事会;

关键词：

False bifurcation; Canard; Delay differential equation; Continuation method; Dynamical system; Mixed-mode oscillations; Neural-field model; Absence epilepsy; PERIODIC-SOLUTIONS; COLLOCATION;

D O I：

10.1007/s00422-009-0357-y

中图分类号：

TP3 [计算技术、计算机技术];

学科分类号：

0812 ;

摘要：

In this article, we present a method for tracking changes in curvature of limit cycle solutions that arise due to inflection points. In keeping with previous literature, we term these changes false bifurcations, as they appear to be bifurcations when considering a Poincar, section that is tangent to the solution, but in actual fact the deformation of the solution occurs smoothly as a parameter is varied. These types of solutions arise commonly in electroencephalogram models of absence seizures and correspond to the formation of spikes in these models. Tracking these transitions in parameter space allows regions to be defined corresponding to different types of spike and wave dynamics, that may be of use in clinical neuroscience as a means to classify different subtypes of the more general syndrome.

引用

页码：145 / 154

页数：10

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