Subcritical Elliptic Bursting of Bautin Type

DOI10.1137/S003613999833263XzbMath1026.92009MaRDI QIDQ4943911

Eugene M. Izhikevich

Publication date: 19 March 2000

Published in: SIAM Journal on Applied Mathematics (Search for Journal in Brave)

zbMATH Keywords

normal formcanonical modelBautin bifurcationsubcritical Andronov-Hopf bifurcationslow passage effectFitzHugh-Rinzel modelfast threshold modulationFM interactionssubcritical elliptic bursterdouble limit cycle bifurcationsub-Hopf/fold cycle bursterweakly connected networks

Mathematics Subject Classification ID

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Neural biology (92C20) Dynamical systems in biology (37N25) Bifurcation theory for ordinary differential equations (34C23) Qualitative investigation and simulation of ordinary differential equation models (34C60)

Related Items (14)

GWN-INDUCED BURSTING, SPIKING, AND RANDOM SUBTHRESHOLD IMPULSING OSCILLATION BEFORE HOPF BIFURCATIONS IN THE CHAY MODEL ⋮ Synchronization of bursting neurons with a slowly varying d. c. current ⋮ Generic torus canards ⋮ Changes in the criticality of Hopf bifurcations due to certain model reduction techniques in systems with multiple timescales ⋮ Different types of bursting calcium oscillations in non-excitable cells ⋮ Periodically-forced finite networks of heterogeneous globally-coupled oscillators: a low-di\-men\-sion\-al approach ⋮ SYNCHRONIZATION OF REGULAR AND CHAOTIC OSCILLATIONS: THE ROLE OF LOCAL DIVERGENCE AND THE SLOW PASSAGE EFFECT — A Case Study on Calcium Oscillations ⋮ A DESIGN METHOD OF BURSTING USING TWO-PARAMETER BIFURCATION DIAGRAMS IN FITZHUGH–NAGUMO MODEL ⋮ Delayed Hopf bifurcation in time-delayed slow-fast systems ⋮ NEURAL EXCITABILITY, SPIKING AND BURSTING ⋮ Controlling a neuron by stimulating a coupled neuron ⋮ Canonical models for torus canards in elliptic bursters ⋮ Codimension two bifurcations of discrete Bonhoeffer-van der Pol oscillator model ⋮ An elementary model of torus canards

This page was built for publication: Subcritical Elliptic Bursting of Bautin Type