Bifurcation phenomena in FitzHugh's nerve conduction equations

DOI10.1016/0022-247X(76)90187-6zbMath0329.92001MaRDI QIDQ1227674

William C. Troy

Publication date: 1976

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Mathematics Subject Classification ID

General biology and biomathematics (92B05) Stability theory for ordinary differential equations (34D99)

Related Items (14)

Parameter-dependent transitions and the optimal control of dynamical diseases ⋮ A higher-order Hopf bifurcation formula and its application to Fitzhugh's nerve conduction equation ⋮ Dynamic behaviors of the FitzHugh-Nagumo neuron model with state-dependent impulsive effects ⋮ Ljapunov approach to multiple Hopf bifurcation ⋮ Bifurcation and resonance in a model for bursting nerve cells ⋮ Multiple limit cycles in predator-prey models ⋮ On the dynamical behaviour of FitzHugh-Nagumo systems: revisited ⋮ The electrical coupling of two simple oscillators: Load and acceleration effects ⋮ Two and three dimensional reductions of the Hodgkin-Huxley system: Separation of time scales and bifurcation schemes ⋮ AN ANALYTIC PICTURE OF NEURON OSCILLATIONS ⋮ Calcium wave propagation by calcium-induced calcium release: An unusual excitable system ⋮ Coherent neural oscillations induced by weak synaptic noise ⋮ ASYMPTOTIC SYNCHRONIZATION IN NETWORKS OF LOCALLY CONNECTED OSCILLATORS ⋮ The number of limit cycles of the FitzHugh nerve system

Cites Work

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• An applicable Hopf bifurcation formula and instability of small periodic solutions of the Field-Noyes model
• A model equation arising from chemical reactor theory
• On the theory and application of the Hopf-Friedrich Bifurcation theory
• 23.—Oscillation Phenomena in the Hodgkin-Huxley Equations
• On the Nature of the Spectrum of Singular Second Order Linear Differential Equations

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