Global Isochrons and Phase Sensitivity of Bursting Neurons
From MaRDI portal
Publication:2876673
DOI10.1137/130931151zbMath1323.92048OpenAlexW1964810201MaRDI QIDQ2876673
Igor Mezić, Blane Rhoads, Jeff Moehlis, Alexandre Mauroy
Publication date: 19 August 2014
Published in: SIAM Journal on Applied Dynamical Systems (Search for Journal in Brave)
Full work available at URL: https://semanticscholar.org/paper/4e7ce9d27760830b7729b514dacebbbda3c02905
Neural biology (92C20) Dynamical systems in biology (37N25) Dynamics induced by flows and semiflows (37C10) Numerical problems in dynamical systems (65P99)
Related Items
Forward-Time and Backward-Time Isochrons and Their Interactions, Extreme phase sensitivity in systems with fractal isochrons, A Continuation Approach to Computing Phase Resetting Curves, Phase reduction and phase-based optimal control for biological systems: a tutorial, Phase-amplitude reduction of transient dynamics far from attractors for limit-cycling systems, Interactions of multiple rhythms in a biophysical network of neurons
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Cross-currents between biology and mathematics: the codimension of pseudo-plateau bursting
- Chemical oscillations, waves, and turbulence
- Mathematical foundations of neuroscience
- Dissection of a model for neuronal parabolic bursting
- Isochrons and phaseless sets
- Patterns of phase compromise in biological cycles
- Mathematical physiology
- Topological and phenomenological classification of bursting oscillations
- Comparison of systems with complex behavior
- Phase-amplitude descriptions of neural oscillator models
- Phase-amplitude response functions for transient-state stimuli
- Synchronization of Elliptic Bursters
- Computation of Limit Cycles and Their Isochrons: Fast Algorithms and Their Convergence
- Modeling the Modulation of Neuronal Bursting: A Singularity Theory Approach
- On the use of Fourier averages to compute the global isochrons of (quasi)periodic dynamics
- Applied Koopmanism
- Continuation-based Computation of Global Isochrons
- Sensitivity Analysis of Oscillator Models in the Space of Phase-Response Curves: Oscillators As Open Systems
- A Computational and Geometric Approach to Phase Resetting Curves and Surfaces
- Dissecting the Phase Response of a Model Bursting Neuron
- Bursting Oscillations Induced by Small Noise
- Oscillator Death in Systems of Coupled Neural Oscillators
- Effects of noise on elliptic bursters
- On the Phase Reduction and Response Dynamics of Neural Oscillator Populations
- Computing Slow Manifolds of Saddle Type
- METHODS OF THE QUALITATIVE THEORY FOR THE HINDMARSH–ROSE MODEL: A CASE STUDY – A TUTORIAL
- Computation of the Phase Response Curve: A Direct Numerical Approach
- NEURAL EXCITABILITY, SPIKING AND BURSTING
- Chaotic Dynamics
- The geometry of biological time.
