CLASSIFICATION OF BURSTING MAPPINGS
From MaRDI portal
Publication:5474139
DOI10.1142/S0218127404011739zbMath1091.37524MaRDI QIDQ5474139
Frank C. Hoppensteadt, Eugene M. Izhikevich
Publication date: 23 June 2006
Published in: International Journal of Bifurcation and Chaos (Search for Journal in Brave)
Neural biology (92C20) Dynamical systems in biology (37N25) Bifurcations of limit cycles and periodic orbits in dynamical systems (37G15) Dynamical systems involving maps of the interval (37E05) Hyperbolic singular points with homoclinic trajectories in dynamical systems (37G20)
Related Items
Complex periodic bursting structures in the Rayleigh-van der Pol-Duffing oscillator ⋮ Non-Gaussian noise and autapse-induced inverse stochastic resonance in bistable Izhikevich neural system under electromagnetic induction ⋮ Development of spiral wave in a regular network of excitatory neurons due to stochastic poisoning of ion channels ⋮ One-dimensional map-based neuron model: a logistic modification ⋮ Inverse period-doubling bifurcations determine complex structure of bursting in a one-dimensional non-autonomous map ⋮ Effects of extracellular electric fields on electrical activities of two-compartment autaptic-neurons ⋮ Discrete geometric singular perturbation theory ⋮ Bursting Transition Dynamics Within the Pre-Bötzinger Complex ⋮ Complete dynamical analysis of a neuron under magnetic flow effect ⋮ Subthreshold oscillations in a map-based neuron model ⋮ Periodic and chaotic dynamics in a map‐based neuron model ⋮ Linking dynamical and functional properties of intrinsically bursting neurons ⋮ Stochastic Spiking-Bursting Excitability and Transition to Chaos in a Discrete-Time Neuron Model ⋮ Bursting Types and Bifurcation Analysis in the Pre-Bötzinger Complex Respiratory Rhythm Neuron ⋮ Analysis of noise effects in a map-based neuron model with Canard-type quasiperiodic oscillations ⋮ Burst mechanisms and burst synchronization in a system of coupled type-I and type-II neurons ⋮ Synchronization and propagation of bursts in networks of coupled map neurons ⋮ A computational model of the mammalian external tufted cell ⋮ FOLD–HOPF BIFURCATIONS OF THE ROSE–HINDMARSH MODEL WITH TIME DELAY ⋮ BURSTING TYPES AND STABLE DOMAINS OF RULKOV NEURON NETWORK WITH MEAN FIELD COUPLING ⋮ Synchronization Dynamics of Two Heterogeneous Chaotic Rulkov Neurons with Electrical Synapses ⋮ Horseshoe in a class of planar mappings ⋮ Bifurcations and fast-slow behaviors in a hyperchaotic dynamical system ⋮ Bursting and synchronization transition in the coupled modified ML neurons ⋮ Stochastic sensitivity of attractors for a piecewise smooth neuron model ⋮ Bifurcation analysis on delay-induced bursting in a shape memory alloy oscillator with time delay feedback ⋮ A Hénon-like map inspired by the generalized discrete-time Fitzhugh-Nagumo model ⋮ Bursting mechanism in a time-delayed oscillator with slowly varying external forcing ⋮ Chaotic oscillations in a map-based model of neural activity ⋮ Chaotic phase synchronization in a modular neuronal network of small-world subnetworks ⋮ A simple one-dimensional map-based model of spiking neurons with wide ranges of firing rates and complexities ⋮ Boundary-Crisis-Induced Complex Bursting Patterns in a Forced Cubic Map
Cites Work
- A two-variable model of somatic-dendritic interactions in a bursting neuron
- Generic excitable dynamics on a two-dimensional map
- Topological and phenomenological classification of bursting oscillations
- Subthreshold oscillations in a map-based neuron model
- Synchronization of Elliptic Bursters
- MODELING NEURONS BY SIMPLE MAPS
- Chaotic Spikes Arising from a Model of Bursting in Excitable Membranes
- ORIGIN OF CHAOS IN A TWO-DIMENSIONAL MAP MODELING SPIKING-BURSTING NEURAL ACTIVITY
- NEURAL EXCITABILITY, SPIKING AND BURSTING
