Understanding and Distinguishing Three-Time-Scale Oscillations: Case Study in a Coupled Morris--Lecar System

DOI10.1137/140985494zbMath1329.34094OpenAlexW1917539272WikidataQ60154131 ScholiaQ60154131MaRDI QIDQ3192589

Yangyang Wang, Vivien Kirk, Pingyu Nan, Jonathan E. Rubin

Publication date: 13 October 2015

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

Full work available at URL: https://doi.org/10.1137/140985494

zbMATH Keywords

oscillationsfast-slow systemsgeometric singular perturbation theorymultiple time scales

Mathematics Subject Classification ID

Neural biology (92C20) Nonlinear oscillations and coupled oscillators for ordinary differential equations (34C15) Singular perturbations of ordinary differential equations (34D15) Qualitative investigation and simulation of ordinary differential equation models (34C60) Singular perturbations for ordinary differential equations (34E15) Relaxation oscillations for ordinary differential equations (34C26)

Related Items

Neural excitability and singular bifurcations ⋮ Multi-timescale systems and fast-slow analysis ⋮ Singularly perturbed problems with multi-tempo fast variables ⋮ Geometric blow-up for folded limit cycle manifolds in three time-scale systems ⋮ Mathematical birth of early afterdepolarizations in a cardiomyocyte model ⋮ Attractor-state itinerancy in neural circuits with synaptic depression ⋮ Multiple timescale mixed bursting dynamics in a respiratory neuron model ⋮ Pseudo-plateau bursting and mixed-mode oscillations in a model of developing inner hair cells ⋮ Spike-Adding in a Canonical Three-Time-Scale Model: Superslow Explosion and Folded-Saddle Canards ⋮ Timescales and mechanisms of sigh-like bursting and spiking in models of rhythmic respiratory neurons ⋮ Fast-slow bursters in the unfolding of a high codimension singularity and the ultra-slow transitions of classes ⋮ Saddle slow manifolds and canard orbits in \(\mathbb{R}^{4}\) and application to the full Hodgkin-Huxley model ⋮ Canard-Mediated (De)Synchronization in Coupled Phantom Bursters ⋮ Characteristic, completion or matching timescales? An analysis of temporary boundaries in enzyme kinetics ⋮ A Three-Scale Model of Spatio-Temporal Bursting ⋮ Analysis of Interacting Local Oscillation Mechanisms in Three-Timescale Systems

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Cooperation of intrinsic bursting and calcium oscillations underlying activity patterns of model pre-Bötzinger complex neurons
• Three time-scales in an extended Bonhoeffer-van der Pol oscillator
• Multiple timescales, mixed mode oscillations and canards in models of intracellular calcium dynamics
• Mathematical foundations of neuroscience
• Mathematical physiology
• Global competition and local cooperation in a network of neural oscillators
• Dynamics of two mutually coupled slow inhibitory neurons
• Bistable Oscillations Arising from Synaptic Depression
• Multiple Geometric Viewpoints of Mixed Mode Dynamics Associated with Pseudo-plateau Bursting
• Modeling the Modulation of Neuronal Bursting: A Singularity Theory Approach
• À propos de canards (Apropos canards)
• Mixed-Mode Oscillations with Multiple Time Scales
• Mixed-mode oscillations in a three time-scale system of ODEs motivated by a neuronal model
• Mixed-Mode Oscillations in Three Time-Scale Systems: A Prototypical Example
• Mixed-Mode Oscillations in a Multiple Time Scale Phantom Bursting System
• Understanding anomalous delays in a model of intracellular calcium dynamics
• Mathematical Modeling of the GnRH Pulse and Surge Generator