Fitzhugh–Nagumo Equation

The Fitzhugh–Nagumo equation (FHN) is a set of nonlinear differential equations that efficiently describes the excitation of cells through two variables.


ÖZBEKLER, ABDULLAH; Zafer, Ağacık (2010-01-01)
A Picone type formula for second order linear non-selfadjoint impulsive differential equations with discontinuous solutions having fixed moments of impulse actions is derived. Applying the formula, Leighton and Sturm-Picone type comparison theorems as well as several oscillation criteria for impulsive differential equations are obtained.
Duff-Inami-Pope-Sezgin-Stelle Bosonic Membrane Equations as an Involutory System
Satır, Ahmet (Oxford University Press (OUP), 1998-12-1)
Using Cartan's geometric formulation of partial diffential equations in the language of exterior differential forms, it is shown that bosonic membrane equations of Duff-Inami-Pope-Sezgin-Stelle (DIPSS) constitute an involutory system. The symmetries of reformulated DIPSS bosonic membrane equations are studied using three forms, elucidating in this way the previous results concerning Lie-point symmetries (Killing symmetries).
Asymptotic behavior of linear impulsive integro-differential equations
Akhmet, Marat; YILMAZ, Oğuz (Elsevier BV, 2008-08-01)
Asymptotic equilibria of linear integro-differential equations and asymptotic relations between solutions of linear homogeneous impulsive differential equations and those of linear integro-differential equations are established. A new Gronwall-Bellman type lemma for integro-differential inequalities is proved. An example is given to demonstrate the validity of one of the results.
An Application of the rayleigh-ritz method to the integral-equation representation of the one-dimensional schrödinger equation
Kaya, Ruşen; Taşeli, Hasan; Department of Mathematics (2019)
In this thesis, the theory of the relations between differential and integral equations is analyzed and is illustrated by the reformulation of the one-dimensional Schrödinger equation in terms of an integral equation employing the Green’s function. The Rayleigh- Ritz method is applied to the integral-equation formulation of the one-dimensional Schrödinger equation in order to approximate the eigenvalues of the corresponding singular problem within the desired accuracy. The outcomes are compared with those r...
Dynamics of numerical methods for cosymmetric ordinary differential equations
Govorukhin, VN; Tsybulin, VG; Karasözen, Bülent (2001-09-01)
The dynamics of numerical approximation of cosymmetric ordinary differential equations with a continuous family of equilibria is investigated. Nonconservative and Hamiltonian model systems in two dimensions are considered and these systems are integrated with several first-order Runge-Kutta methods. The preservation of symmetry and cosymmetry, the stability of equilibrium points, spurious solutions and transition to chaos are investigated by presenting analytical and numerical results. The overall performan...
Citation Formats
S. Göktepe, Fitzhugh–Nagumo Equation. 2015.