Wild oscillations in a nonlinear neuron model with resets. I: Bursting, spike-adding and chaos

DOI10.3934/dcdsb.2017204zbMath1371.37032arXiv1611.02740OpenAlexW2584351324WikidataQ60154126 ScholiaQ60154126MaRDI QIDQ2405531

Justyna Signerska-Rynkowska, Jonathan E. Rubin, Alexandre Vidal, Jonathan D. Touboul

Publication date: 26 September 2017

Published in: Discrete and Continuous Dynamical Systems. Series B (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1611.02740

zbMATH Keywords

chaosnonlinear dynamicsunimodal mapshybrid dynamical systemsspiking dynamicscomplex oscillationsspike-addingneuronal burstingperiod-incrementing

Mathematics Subject Classification ID

Neural biology (92C20) Dynamical systems in biology (37N25) Periodic orbits of vector fields and flows (37C27) Dynamical systems involving maps of the interval (37E05)

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Cites Work

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• Modeling focal epileptic activity in the Wilson-cowan model with depolarization block
• Lapicque's 1907 paper: from frogs to integrate-and-fire
• Concepts and results in chaotic dynamics. A short course
• Hyperbolicity and invariant measures for general \(C^ 2\) interval maps satisfying the Misiurewicz condition
• Firing patterns in the adaptive exponential integrate-and-fire model
• Dynamics and bifurcations of the adaptive exponential integrate-and-fire model
• On the concept of attractor
• Sensitive dependence to initial conditions for one dimensional maps
• Dynamics in one dimension
• On maps with dense orbits and the definition of chaos
• Reduction of a model of an excitable cell to a one-dimensional map
• Uniqueness and stability of periodic bursting solutions
• Wild Cantor attractors exist
• First return maps for the dynamics of synaptically coupled conditional bursters
• Wild oscillations in a nonlinear neuron model with resets. II: Mixed-mode oscillations
• Time analysis and entry-exit relation near planar turning points
• Periodicity versus Chaos in One-Dimensional Dynamics
• Mixed-mode bursting oscillations: Dynamics created by a slow passage through spike-adding canard explosion in a square-wave burster
• Locally Contractive Dynamics in Generalized Integrate-and-Fire Neurons
• Modeling of spiking-bursting neural behavior using two-dimensional map
• Border Collision Bifurcations of Stroboscopic Maps in Periodically Driven Spiking Models
• Renormalization in one-dimensional dynamics
• Bifurcation Analysis of a General Class of Nonlinear Integrate-and-Fire Neurons
• The Dynamics of Regularized Discontinuous Maps with Applications to Impacting Systems
• Spiking Dynamics of Bidimensional Integrate-and-Fire Neurons
• One-dimensional dynamics: The Schwarzian derivative and beyond
• No Division Implies Chaos
• Measurable dynamics of $S$-unimodal maps of the interval
• On Devaney's Definition of Chaos
• Canard cycles and center manifolds
• Importance of the Cutoff Value in the Quadratic Adaptive Integrate-and-Fire Model
• A Contraction Argument for Two-Dimensional Spiking Neuron Models
• NEURAL EXCITABILITY, SPIKING AND BURSTING
• Bursting
• A Period-Adding Phenomenon
• Ordinary Differential Equations

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