An Introduction to Modeling Neuronal Dynamics

DOI10.1007/978-3-319-51171-9zbMath1382.92001OpenAlexW2605700843MaRDI QIDQ2953575

Christoph Börgers

Publication date: 4 January 2017

Published in: Texts in Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-3-319-51171-9

zbMATH Keywords

synchronizationoscillationsentrainmentsynaptic plasticitysingle neuronmodeling neuronal dynamicsneuronal communication

Mathematics Subject Classification ID

Neural biology (92C20) Dynamical systems in biology (37N25) Dynamics induced by flows and semiflows (37C10) Numerical methods for initial value problems involving ordinary differential equations (65L05) Simulation of dynamical systems (37M05) Fixed points and periodic points of dynamical systems; fixed-point index theory; local dynamics (37C25) Bifurcations of limit cycles and periodic orbits in dynamical systems (37G15) Finite difference and finite volume methods for ordinary differential equations (65L12) Introductory exposition (textbooks, tutorial papers, etc.) pertaining to biology (92-01)

Related Items (16)

Malleability of gamma rhythms enhances population-level correlations ⋮ Existence of limit cycles for a class of quartic polynomial differential system depending on parameters ⋮ Membrane potential resonance in non-oscillatory neurons interacts with synaptic connectivity to produce network oscillations ⋮ Bistability at the onset of neuronal oscillations ⋮ Low-dimensional models of single neurons: a review ⋮ Hopf bifurcations on invariant manifolds of a modified FitzHugh-Nagumo model ⋮ M-current expands the range of gamma frequency inputs to which a neuronal target entrains ⋮ Delay embedding of periodic orbits using a fixed observation function ⋮ The Winfree model with non-infinitesimal phase-response curve: Ott–Antonsen theory ⋮ Switching in Cerebellar Stellate Cell Excitability in Response to a Pair of Inhibitory/Excitatory Presynaptic Inputs: A Dynamical System Perspective ⋮ On Rhythms in Neuronal Networks with Recurrent Excitation ⋮ Delayed loss of stability due to the slow passage through Hopf bifurcations in reaction–diffusion equations ⋮ Coexistence of firing patterns and its control in two neurons coupled through an asymmetric electrical synapse ⋮ Inhibition-based relaxation oscillations emerge in resonator networks ⋮ Constructive role of noise and diffusion in an excitable slow–fast population system ⋮ Motifs for Processes on Networks

Uses Software

• Matlab

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