Approximate explicit analytic solution of the Elenbaas-Heller equation

2016 ◽  
Vol 120 (6) ◽  
pp. 063304 ◽  
Author(s):  
Meng-Ran Liao ◽  
Hui Li ◽  
Wei-Dong Xia
Keyword(s):  
Analytic Solution ◽  
Explicit Analytic Solution

AN ANALYTIC PICTURE OF NEURON OSCILLATIONS

2004 ◽  
Vol 14 (05) ◽  
pp. 1539-1548 ◽  
Author(s):  
PAUL E. PHILLIPSON ◽  
PETER SCHUSTER
Keyword(s):  
Action Potential ◽  
Analytic Solution ◽  
Phase Locking ◽  
Van Der Pol Oscillator ◽  
Close Approximation ◽  
Van Der Pol ◽  
Analytic Expressions ◽  
Nagumo Equations ◽  
Explicit Analytic Solution ◽  
Spiking Model

Current induced oscillations of a space clamped neuron action potential demonstrates a bifurcation scenario originally encapsulated by the four-dimensional Hodgkin–Huxley equations. These oscillations were subsequently described by the two-dimensional FitzHugh–Nagumo Equations in close agreement with the Hodgkin–Huxley theory. It is shown that the FitzHugh–Nagumo equations can to close approximation be reduced to a generalized van der Pol oscillator externally driven by the current. The current functions as an external constant force driving the action potential. As a consequence approximate analytic expressions are derived which predict the bifurcation scenario, the amplitudes of the oscillations and the oscillation periods in terms of the current and the physiological constants of the FitzHugh–Nagumo model. A second reduction permits explicit analytic solution and results in a spiking model which can be multiply coupled and extended to include the dynamics of phase locking, entrainment and chaos characteristic of time-dependent synaptic inputs.

scholarly journals Explicit Analytic Solution of Vibration Equation for large domain by mean of the Elzaki projected Differential Transform Method

2015 ◽  
Vol 11 (5) ◽  
pp. 5244-5257 ◽  
Author(s):  
Muhammad Suleman ◽  
Qingbiao Wu ◽  
TM Elzaki
Keyword(s):  
Analytic Solution ◽  
Initial Conditions ◽  
Numerical Results ◽  
Differential Transform Method ◽  
Series Solutions ◽  
Transform Method ◽  
Vibration Equation ◽  
Differential Transform ◽  
Explicit Analytic Solution ◽  
Explicit Series Solutions

The aim of this paper is to present a reliable and efficient algorithm Elzaki projected differential transform method (EPDTM) to obtain the explicit solution of vibration equation for a very large membrane with given initial conditions. By using initial conditions, explicit series solutions for six different cases have been derived for the fast convergence of the solution. Numerical results show the reliability, efficiency and accuracy of Elzaki projected differential transform method (EPDTM). Numerical results for the six different cases are presented graphically.

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