The global bifurcation structure of the BVP neuronal model driven by periodic pulse trains

DOI10.1016/0025-5564(94)00035-XzbMath0818.92003OpenAlexW2061900451WikidataQ52351067 ScholiaQ52351067MaRDI QIDQ1804873

Shunsuke Sato, Shinji Doi

Publication date: 16 August 1995

Published in: Mathematical Biosciences (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0025-5564(94)00035-x

zbMATH Keywords

chaosperiodic orbitsperiodperiod-doubling bifurcationsFitzHugh-Nagumo neuronal modelPTCstimulus intensityBonhoeffer-van der Pol modelglobal bifurcation structureperiodic pulse trainsphase-transition curve

Mathematics Subject Classification ID

Neural biology (92C20) Neural networks for/in biological studies, artificial life and related topics (92B20) Applications of dynamical systems (37N99)

Related Items

Complex mixed-mode oscillations in a Bonhoeffer-van der Pol oscillator under weak periodic perturbation ⋮ Dynamic behaviors of the FitzHugh-Nagumo neuron model with state-dependent impulsive effects ⋮ A method for Lyapunov spectrum estimation using cloned dynamics and its application to the discontinuously-excited FitzHugh-Nagumo model ⋮ Continuation and bifurcation analysis of a periodically forced excitable system ⋮ Nested mixed-mode oscillations ⋮ Extending the Concept of Isochrons from Oscillatory to Excitable Systems for Modeling an Excitable Neuron ⋮ MODE LOCKING IN A SPATIALLY EXTENDED NEURON MODEL: ACTIVE SOMA AND COMPARTMENTAL TREE ⋮ SEARCHING FOR SPECIFIC PERIODIC AND CHAOTIC OSCILLATIONS IN A PERIODICALLY-EXCITED HODGKIN–HUXLEY MODEL ⋮ Nested mixed-mode oscillations in a canard-generating driven Bonhoeffer-van der Pol oscillator ⋮ Forced excitations and excitable chaos in the photosensitive Oregonator under periodic sinusoidal perturbations ⋮ Bifurcation structure of a periodically driven nerve pulse equation modelling cardiac conduction ⋮ Noise-induced critical breakdown of phase lockings in a forced van der Pol oscillator ⋮ Threshold, excitability and isochrones in the Bonhoeffer–van der Pol system ⋮ Nested mixed-mode oscillations. II: Experimental and numerical study of a classical Bonhoeffer-van der Pol oscillator

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Global bifurcation structure in periodically stimulated giant axons of squid
• Nonlinear oscillations, dynamical systems, and bifurcations of vector fields
• On periodic responses of a mathematical neuron model
• On periodic responses generated by a degenerate analog neuron model with periodic inputs
• Period-doubling bifurcations, chaos, phase-locking and devil's staircase in a Bonhoeffer-van der Pol oscillator
• Pulse sequences generated by a degenerate analog neuron model
• Isochrons and phaseless sets
• Generation of the nervous impulse and periodic oscillations
• On periodic orbits of trapezoid maps
• A Bonhoeffer-van der Pol oscillator model of locked and non-locked behaviors of living pacemaker neurons
• Response characteristics of the BVP neuron model to periodic pulse inputs
• A one-variable map analysis of bursting in the Belousov-Zhabotinskiĭ reaction
• Chaotic Behavior in Piecewise Continuous Difference Equations
• Response characteristics of a neuron model to a periodic input
• On a response characteristic of a mathematical neuron model