FITZHUGH–NAGUMO REVISITED: TYPES OF BIFURCATIONS, PERIODICAL FORCING AND STABILITY REGIONS BY A LYAPUNOV FUNCTIONAL

DOI10.1142/S0218127404009685zbMath1100.34031OpenAlexW1992450291MaRDI QIDQ4655608

Tanya V. Kostova, Renuka Ravindran, Maria Elena Schonbek

Publication date: 8 March 2005

Published in: International Journal of Bifurcation and Chaos (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/s0218127404009685

zbMATH Keywords

homoclinic bifurcationperiodic forcingFitzHugh-Nagumosubcritical and supercritical Hopf bifurcation

Mathematics Subject Classification ID

Periodic solutions to ordinary differential equations (34C25) Neural biology (92C20) Dynamical systems in biology (37N25) Bifurcation theory for ordinary differential equations (34C23) Bifurcations of limit cycles and periodic orbits in dynamical systems (37G15) Qualitative investigation and simulation of ordinary differential equation models (34C60) Asymptotic properties of solutions to ordinary differential equations (34D05)

Related Items (15)

An explicit nonstandard finite difference scheme for the FitzHugh–Nagumo equations ⋮ Model reduction of dynamical systems by proper orthogonal decomposition: error bounds and comparison of methods using snapshots from the solution and the time derivatives ⋮ Liouvillian integrability of the FitzHugh-Nagumo systems ⋮ Attraction basin of the equilibrium configuration in the FitzHugh-Nagumo model ⋮ Recurrence quantification and bifurcation analysis of electrical activity in resistive/memristive synapse coupled FitzHugh-Nagumo type neurons ⋮ Stable discontinuous stationary solutions to reaction-diffusion-ODE systems ⋮ Synchronization of coupled chaotic FitzHugh-Nagumo neurons via Lyapunov functions ⋮ Approximation of continuous surface differential operators with the generalized moving least-squares (GMLS) method for solving reaction-diffusion equation ⋮ On the dynamical behaviour of FitzHugh-Nagumo systems: revisited ⋮ A study on nonnegativity preservation in finite element approximation of Nagumo-type nonlinear differential equations ⋮ Oscillation patterns in tori of modified FHN neurons ⋮ Periodic Solutions of a Periodic FitzHugh–Nagumo System ⋮ Steady states of FitzHugh-Nagumo system with non-diffusive activator and diffusive inhibitor ⋮ Entrainment by chaos ⋮ Traveling Waves Impulses of FitzHugh Model with Diffusion and Cross-Diffusion

Cites Work

• Unnamed Item
• On a four parameter family of planar vector fields
• Period-doubling bifurcations, chaos, phase-locking and devil's staircase in a Bonhoeffer-van der Pol oscillator
• Response characteristics of the BVP neuron model to periodic pulse inputs
• VODE: A Variable-Coefficient ODE Solver

This page was built for publication: FITZHUGH–NAGUMO REVISITED: TYPES OF BIFURCATIONS, PERIODICAL FORCING AND STABILITY REGIONS BY A LYAPUNOV FUNCTIONAL