Bottom-up approach to torus bifurcation in neuron models
From MaRDI portal
Publication:4556555
DOI10.1063/1.5042078zbMath1466.92022arXiv1805.11719OpenAlexW3104614380WikidataQ58590107 ScholiaQ58590107MaRDI QIDQ4556555
Huiwen Ju, Alexander B. Neiman, Andrej L. Shil'nikov
Publication date: 16 November 2018
Published in: Chaos: An Interdisciplinary Journal of Nonlinear Science (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1805.11719
Related Items (11)
Stochastic spiking-bursting transitions in a neural birhythmic 3D model with the Lukyanov-Shilnikov bifurcation ⋮ Computational analysis of a 9D model for a small DRG neuron ⋮ A survey on the blow-up method for fast-slow systems ⋮ How noise transforms spiking into bursting in a neuron model having the Lukyanov-Shilnikov bifurcation ⋮ Noise-induced toroidal excitability in neuron model ⋮ Dynamics of a neuron-glia system: the occurrence of seizures and the influence of electroconvulsive stimuli. A mathematical and numerical study ⋮ Dynamics and bifurcations in multistable 3-cell neural networks ⋮ Dynamics of coupled generators of quasiperiodic oscillations: different types of synchronization and other phenomena ⋮ Stochastic Bifurcations, Chaos and Phantom Attractors in the Langford System with Tori ⋮ Canonical models for torus canards in elliptic bursters ⋮ Dynamic mechanism of multiple bursting patterns in a whole-cell multiscale model with calcium oscillations
Uses Software
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Mathematical foundations of neuroscience
- Dynamical systems VII. Integrable systems. Nonholonomic dynamical systems. Transl. from the Russian by A.G. Reyman and M.A. Semenov-Tian- Shansky
- The transition from bursting to continuous spiking in excitable membrane models
- Generic torus canards
- Complete dynamical analysis of a neuron model
- Stability of the stationary solutions of neural field equations with propagation delays
- A phenomenological model of seizure initiation suggests network structure may explain seizure frequency in idiopathic generalised epilepsy
- Voltage interval mappings for activity transitions in neuron models for elliptic bursters
- Subthreshold oscillations in a map-based neuron model
- GLOBAL TANGENCY AND TRANSVERSALITY OF PERIODIC FLOWS AND CHAOS IN A PERIODICALLY FORCED, DAMPED DUFFING OSCILLATOR
- BIFURCATION AND PREDICTABILITY ANALYSIS OF A LOW-ORDER ATMOSPHERIC CIRCULATION MODEL
- Homoclinic bifurcation in a Hodgkin–Huxley model of thermally sensitive neurons
- ORIGIN OF CHAOS IN A TWO-DIMENSIONAL MAP MODELING SPIKING-BURSTING NEURAL ACTIVITY
- ON SOME MATHEMATICAL TOPICS IN CLASSICAL SYNCHRONIZATION.: A TUTORIAL
- An elementary model of torus canards
- MATCONT
- NEURAL EXCITABILITY, SPIKING AND BURSTING
This page was built for publication: Bottom-up approach to torus bifurcation in neuron models