Ergodicity and spike rate for stochastic FitzHugh-Nagumo neural model with periodic forcing

DOI10.1016/j.chaos.2019.04.014zbMath1448.60130OpenAlexW2942462549WikidataQ128029374 ScholiaQ128029374MaRDI QIDQ2213642

Kenneth Uda

Publication date: 2 December 2020

Published in: Chaos, Solitons and Fractals (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.chaos.2019.04.014

zbMATH Keywords

random dynamical systemsrandom periodic solutionsaction potentialsstochastic FitzHugh-Nagumo model

Mathematics Subject Classification ID

Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) Neural networks for/in biological studies, artificial life and related topics (92B20) Ergodicity, mixing, rates of mixing (37A25) Resonance phenomena for ordinary differential equations involving randomness (34F15)

Related Items (4)

Random periodic solutions for a class of hybrid stochastic differential equations ⋮ Synchronization for fractional FitzHugh–Nagumo equations with fractional Brownian motion ⋮ Non‐instantaneous impulsive stochastic FitzHugh–Nagumo equation with fractional Brownian motion ⋮ Stochastic Sensitivity and Method of Principal Directions in Excitability Analysis of the Hodgkin–Huxley Model

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Large deviations in fast-slow systems
• Random periodic solutions of SPDEs via integral equations and Wiener-Sobolev compact embedding
• Pathwise random periodic solutions of stochastic differential equations
• Double averaging principle for periodically forced stochastic slow-fast systems
• Suppression of noise in Fitzhugh-Nagumo model driven by a strong periodic signal
• Dynamics of a FitzHugh-Nagumo system subjected to autocorrelated noise
• Random periodic solutions of random dynamical systems
• Effect of noise and perturbations on limit cycle systems
• Dirichlet forms and analysis on Wiener space
• Stochastic resonance in neuron models
• Perfect cocycles through stochastic differential equations
• Analytical and simulation results for stochastic Fitzhugh-Nagumo neurons and neural networks
• Escape from a metastable state with fluctuating barrier
• Elimination of fast chaotic degrees of freedom: on the accuracy of the Born approximation
• Hypoelliptic stochastic Fitzhugh-Nagumo neuronal model: mixing, up-crossing and estimation of the spike rate
• The exit problem for diffusions with time-periodic drift and stochastic resonance
• Multiscale analysis of slow-fast neuronal learning models with noise
• Goodness-of-fit tests and nonparametric adaptive estimation for spike train analysis
• Ergodicity for SDEs and approximations: locally Lipschitz vector fields and degenerate noise.
• Stochastic modelling: replacing fast degrees of freedom by noise
• Existence of random invariant periodic curves via random semiuniform ergodic theorem
• Stability of Markovian processes II: continuous-time processes and sampled chains
• Stability of Markovian processes III: Foster–Lyapunov criteria for continuous-time processes
• Stratonovich and Ito Stochastic Taylor Expansions
• Level Sets and Extrema of Random Processes and Fields
• An investigation of two-dimensional parameter-induced stochastic resonance and applications in nonlinear image processing
• ON LARGE DEVIATIONS IN THE AVERAGING PRINCIPLE FOR STOCHASTIC DIFFERENTIAL EQUATIONS WITH PERIODIC COEFFICIENTS. II
• L² Diffusion Approximation for Slow Motion in Averaging
• Reduction of deterministic coupled atmosphere–ocean models to stochastic ocean models: a numerical case study of the Lorenz–Maas system
• A random dynamical systems perspective on stochastic resonance
• Stochastic Processes and Applications
• Mathematical Analysis of Random Noise

This page was built for publication: Ergodicity and spike rate for stochastic FitzHugh-Nagumo neural model with periodic forcing