Geometry of Mixed-Mode Oscillations in the 3-D Autocatalator
From MaRDI portal
Publication:4936248
DOI10.1142/S0218127498000322zbMath0933.92036OpenAlexW2002570644MaRDI QIDQ4936248
Helwig Löffelmann, Alexandra Milik, Eduard Gröller, Peter Szmolyan
Publication date: 25 January 2000
Published in: International Journal of Bifurcation and Chaos (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1142/s0218127498000322
Classical flows, reactions, etc. in chemistry (92E20) Dynamical systems in biology (37N25) Singular perturbations of ordinary differential equations (34D15)
Related Items
Mixed mode oscillations induced by bi-stability and fractal basins in the FGP plate under slow parametric and resonant external excitations, Slow-fast dynamics in the truss core sandwich plate under excitations with high and low frequencies, À propos de canards (Apropos canards), Relaxation oscillations in \({\mathbb R}^3\), Multimodal regimes in a compartmental model of the dopamine neuron, First return maps for the dynamics of synaptically coupled conditional bursters, Bifurcations of mixed-mode oscillations in a stellate cell model, Spike-frequency adaptation of a two-compartment neuron modulated by extracellular electric fields, On the Nonexistence of Terrestrial Canards: Linking Canards and Rivers, A survey on the blow-up method for fast-slow systems, Multimodal oscillations in systems with strong contraction, Canards of Folded Saddle-Node Type I, Complex mixed-mode oscillations in a Bonhoeffer-van der Pol oscillator under weak periodic perturbation, Noise-induced Canard and Mixed-Mode Oscillations in Large-Scale Stochastic Networks, Morphogen-directed cell fate boundaries: slow passage through bifurcation and the role of folded saddles, Bursting Oscillations and Mixed-Mode Oscillations in Driven Liénard System, Period-doubling cascades of canards from the extended Bonhoeffer-van der Pol oscillator, Mixed-Mode Oscillations and Twin Canard Orbits in an Autocatalytic Chemical Reaction, Global stability of the attracting set of an enzyme-catalysed reaction system, Mixed-mode oscillations and chaos from a simple second-order oscillator under weak periodic perturbation, Computing the Stable Manifold of a Saddle Slow Manifold, Polynomial normal forms of constrained differential equations with three parameters, Mixed mode oscillations and phase locking in coupled FitzHugh-Nagumo model neurons, Giant squid-hidden canard: the 3D geometry of the Hodgkin-Huxley model, A Surface of Heteroclinic Connections Between Two Saddle Slow Manifolds in the Olsen Model, Mixed-mode oscillations in a three time-scale model for the dopaminergic neuron, Mixed-mode oscillations and slow manifolds in the self-coupled FitzHugh-Nagumo system, Localized and asynchronous patterns via canards in coupled calcium oscillators, Local analysis near a folded saddle-node singularity, Reduction of a model of an excitable cell to a one-dimensional map, Mixed-mode bursting oscillations: Dynamics created by a slow passage through spike-adding canard explosion in a square-wave burster, Saddle slow manifolds and canard orbits in \(\mathbb{R}^{4}\) and application to the full Hodgkin-Huxley model, Mixed-mode oscillations in a three time-scale system of ODEs motivated by a neuronal model, Incomplete approach to homoclinicity in a model with bent-slow manifold geometry, From random Poincaré maps to stochastic mixed-mode-oscillation patterns, On decomposing mixed-mode oscillations and their return maps, Mixed mode oscillations in a conceptual climate model
Cites Work
- Geometric singular perturbation theory for ordinary differential equations
- On the instability of duck-cycles arising during the passage of an equilibrium of a multidimensional relaxation system through the disruption manifold
- Genealogy and Bifurcation Skeleton for Cycles of the Iterated Two-Extremum Map of the Interval
- Chaos via mixed-mode oscillations
- Singular Hopf Bifurcation to Relaxation Oscillations
- Relaxation oscillations including a standard chase on French ducks