Interaction of Canard and Singular Hopf Mechanisms in a Neural Model

DOI10.1137/110823171zbMath1241.34058OpenAlexW2022543096WikidataQ60154134 ScholiaQ60154134MaRDI QIDQ5388646

Rodica Curtu, Jonathan E. Rubin

Publication date: 19 April 2012

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

Full work available at URL: https://doi.org/10.1137/110823171

zbMATH Keywords

inhibitionmixed-mode oscillationscanardsneural competitionsingular Hopf bifurcation

Mathematics Subject Classification ID

Neural biology (92C20) Geometric methods in ordinary differential equations (34A26) Bifurcation theory for ordinary differential equations (34C23) Singular perturbations of ordinary differential equations (34D15) Singular perturbations, turning point theory, WKB methods for ordinary differential equations (34E20) Qualitative investigation and simulation of ordinary differential equation models (34C60) Canard solutions to ordinary differential equations (34E17)

Related Items (15)

Canard solutions in neural mass models: consequences on critical regimes ⋮ On the Nonexistence of Terrestrial Canards: Linking Canards and Rivers ⋮ On the periodic orbit bifurcating from a zero Hopf bifurcation in systems with two slow and one fast variables ⋮ Canards of Folded Saddle-Node Type I ⋮ Noise-induced Canard and Mixed-Mode Oscillations in Large-Scale Stochastic Networks ⋮ Canard-induced complex oscillations in an excitatory network ⋮ Membrane potential resonance in non-oscillatory neurons interacts with synaptic connectivity to produce network oscillations ⋮ Symmetric bursting behaviors in the generalized FitzHugh-Nagumo model ⋮ Mixed-Mode Oscillations in Coupled FitzHugh–Nagumo Oscillators: Blow-Up Analysis of Cusped Singularities ⋮ Methods to assess binocular rivalry with periodic stimuli ⋮ Mixed mode oscillations and phase locking in coupled FitzHugh-Nagumo model neurons ⋮ Three time-scales in an extended Bonhoeffer-van der Pol oscillator ⋮ Complex oscillatory patterns near singular Hopf bifurcation in a two-timescale ecosystem ⋮ Inhibition-based relaxation oscillations emerge in resonator networks ⋮ Analysis of Interacting Local Oscillation Mechanisms in Three-Timescale Systems

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