Zero-Hopf bifurcation in the FitzHugh-Nagumo system

DOI10.1002/mma.3365zbMath1337.37036arXiv1404.0612OpenAlexW2116579303MaRDI QIDQ2795430

Rodrigo D. Euzébio, Jaume Llibre, Claudio Vidal

Publication date: 21 March 2016

Published in: Mathematical Methods in the Applied Sciences (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1404.0612

zbMATH Keywords

periodic orbitaveraging theoryzero-Hopf bifurcationFitzhugh-Nagumo system

Mathematics Subject Classification ID

Bifurcations of singular points in dynamical systems (37G10) Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert's 16th problem and ramifications) for ordinary differential equations (34C07) Bifurcations of limit cycles and periodic orbits in dynamical systems (37G15) Methods of ordinary differential equations applied to PDEs (35A24)

Related Items

On the integrability problem for the Hopf-zero singularity and its relation with the inverse Jacobi multiplier, New results on averaging theory and applications, Orbital normal forms for a class of three-dimensional systems with an application to Hopf-zero bifurcation analysis of Fitzhugh-Nagumo system, The integrability and the zero-Hopf bifurcation of the three dimensional Lotka-Volterra systems, Degenerate Fold–Hopf Bifurcations in a Rössler-Type System

Cites Work

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• On the Hopf-zero bifurcation of the Michelson system
• Breakdown of heteroclinic orbits for some analytic unfoldings of the Hopf-zero singularity
• On the dynamical behaviour of FitzHugh-Nagumo systems: revisited
• The inner equation for generic analytic unfoldings of the Hopf-zero singularity
• Analytic first integrals of the FitzHugh-Nagumo systems
• Homoclinic orbits of the FitzHugh-Nagumo equation: the singular-limit
• Averaging methods for finding periodic orbits via Brouwer degree.
• Existence of wavefronts and impulses to FitzHugh-Nagumo equations
• The entwined wiggling of homoclinic curves emerging from saddle-node/Hopf instabilities
• Computer-aided experiments on the Hopf bifurcation of the FitzHugh-Nagumo nerve model
• Bifurcation to Quasi-Periodic Tori in the Interaction of Steady State and Hopf Bifurcations
• Subordinate Šil'nikov bifurcations near some singularities of vector fields having low codimension
• Homoclinic Orbits of the FitzHugh–Nagumo Equation: Bifurcations in the Full System
• Limit cycles bifurcating from a non-isolated zero-Hopf equilibrium of three-dimensional differential systems
• Elements of applied bifurcation theory