TY - JOUR
T1 - Genesis of bursting oscillations in the Hindmarsh-Rose model and homoclinicity to a chaotic saddle
AU - Wang, X. J.
N1 - Funding Information:
It is a pleasuret o thank J. Rinzel, D. Terman and A. Sherman for explainingt o me their recent work, and for interestingd iscussionos n the subject treated here. This work is partly supported by the Office of Naval Research under the contractN o. N00014-90J-1194T. he numerical simulationsw ere carried out on the National Cancer Institute Advanced ScientificC omputing Laboratory.
PY - 1993/1/30
Y1 - 1993/1/30
N2 - We present two hypotheses on the mathematical mechanism underlying bursting dynamics in a class of differential systems: (1) that the transition from continuous firing of spikes to bursting is caused by a crisis which destabilizes a chaotic state of continuous spiking; and (2) that the bursting corresponds to a homoclinicity to this unstable chaotic state. These propositions are supported by a numerical test on the Hindmarsh-Rose model, a prototype of its kind. We conclude by a unified view for three types of complex multi-modal oscillations: homoclinic systems, bursting, and the Pomeau-Manneville intermittency.
AB - We present two hypotheses on the mathematical mechanism underlying bursting dynamics in a class of differential systems: (1) that the transition from continuous firing of spikes to bursting is caused by a crisis which destabilizes a chaotic state of continuous spiking; and (2) that the bursting corresponds to a homoclinicity to this unstable chaotic state. These propositions are supported by a numerical test on the Hindmarsh-Rose model, a prototype of its kind. We conclude by a unified view for three types of complex multi-modal oscillations: homoclinic systems, bursting, and the Pomeau-Manneville intermittency.
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U2 - 10.1016/0167-2789(93)90286-A
DO - 10.1016/0167-2789(93)90286-A
M3 - Article
AN - SCOPUS:44949266418
SN - 0167-2789
VL - 62
SP - 263
EP - 274
JO - Physica D: Nonlinear Phenomena
JF - Physica D: Nonlinear Phenomena
IS - 1-4
ER -