Publication
Title
Codimension-two homoclinic bifurcations underlying spike adding in the Hindmarsh-rose burster
Author
Abstract
The Hindmarsh-Rose model of neural action potential is revisited from the point of view of global bifurcation analysis, with the singular perturbation parameter held fixed. Of particular concern is a parameter regime where lobe-shaped regions of irregular bursting undergo a transition to stripe-shaped regions of periodic bursting. The boundary of each stripe represents a fold bifurcation that causes a smooth spike adding transition where the number of spikes in each burst is increased by one. It is shown via numerical path-following that the lobe-to-stripe transition is organized by a sequence of codimension-one and -two homoclinic bifurcations. Specifically, each of a sequence of homoclinic bifurcation curves in the parameter plane is found to undergo a sharp turn, due to interaction between a two-dimensional unstable manifold and the one-dimensional slow manifold that persists from the singular limit. Local analysis using approximate Poincare maps shows that each turning point induces an inclination-flip bifurcation that gives birth to the fold curve that organizes the spike adding transition. Implications of this mechanism for other excitable systems are discussed.
Language
English
Source (journal)
SIAM journal on applied dynamical systems. - Philadelphia, Pa
Publication
Philadelphia, Pa : 2012
ISSN
1536-0040
Volume/pages
11:3(2012), p. 939-962
ISI
000309977400006
Full text (Publisher's DOI)
UAntwerpen
Faculty/Department
Research group
Publication type
Subject
Affiliation
Publications with a UAntwerp address
External links
Web of Science
Record
Identification
Creation 06.12.2012
Last edited 16.07.2017
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