Continuation and bifurcation analysis of a periodically forced excitable system

DOI10.1016/j.jtbi.2007.01.017zbMath1451.92068OpenAlexW2064563556WikidataQ79872361 ScholiaQ79872361MaRDI QIDQ2210067

H. Croisier, Pierre C. Dauby

Publication date: 5 November 2020

Published in: Journal of Theoretical Biology (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jtbi.2007.01.017

zbMATH Keywords

bifurcation diagramcontinuationFitzhugh-Nagumo systemperiodic pacingexcitable cell

Mathematics Subject Classification ID

Periodic solutions to ordinary differential equations (34C25) Neural biology (92C20) Bifurcation theory for ordinary differential equations (34C23)

Uses Software

• AUTO

Cites Work

• Unnamed Item
• Global bifurcation structure in periodically stimulated giant axons of squid
• Phase locking, period doubling bifurcations and chaos in a mathematical model of a periodically driven oscillator: A theory for the entrainment of biological oscillators and the generation of cardiac dysrhythmias
• Subharmonic resonance and chaos in forced excitable systems
• Response characteristics of the BVP neuron model to periodic pulse inputs
• The global bifurcation structure of the BVP neuronal model driven by periodic pulse trains
• Resonance in excitable systems under step-function forcing. II: Subharmonic solutions and persistence
• Periodic stimulus and the single cardiac cell -- getting more out of 1D maps
• Hysteresis and bistability in the direct transition from 1:1 to 2:1 rhythm in periodically driven single ventricular cells
• On the Resonance Structure in a Forced Excitable System
• NUMERICAL ANALYSIS AND CONTROL OF BIFURCATION PROBLEMS (II): BIFURCATION IN INFINITE DIMENSIONS
• Extending the Concept of Isochrons from Oscillatory to Excitable Systems for Modeling an Excitable Neuron

This page was built for publication: Continuation and bifurcation analysis of a periodically forced excitable system