Institutul de Matematică şi Informatică "Vladimir Andrunachievici"
Universitatea de Stat din MoldovaRO EN
A closed form asymptotic solution for the FitzHugh-Nagumo model.
Authors: Adelina Georgescu, Gheorghe Nistor, Marin-Nicolae Popescu, Dinel Popa
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Abstract
By means of a change of unknown function and independent variable, the Cauchy problem of singular perturbation from electrophysiology, known as the FitzHugh-Nagumo model, is reduced to a regular perturbation problem (Section 1). Then, by applying the regular perturbation technique to the last problem and using an existence, uniqueness and asymptotic behavior theorem of the second and third author, the models of asymptotic approximation of an arbitrary order are deduced (Section 2). The closed-form expressions for the solution of the model of first order asymptotic approximation and for the time along the phase trajectories are derived in Section 3. In Section 4, by applying several times the method of variation of coefficients and prime integrals, the closed-form solution of the model of second order asymptotic approximation is found. The results from this paper served to the author to study (elsewhere) the relaxation oscillations versus the oscillations in two and three times corresponding to concave limit cycles (canards).E-mail:
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Contents
- Fuzzy subquasigroups with respect to a s-norm.
- Ideal Theory in Commutative Semirings.
- A closed form asymptotic solution for the FitzHugh-Nagumo model.
- Non-fundamental 2-isohedral tilings of the sphere.
- Discrete Optimal Control Problem with Varying Time of States Transactions of Dynamical System and Algorithm for its solving.
- Measure of quasistability of a vector integer linear programming problem with generalized principle of optimality in the Helder metric.
- Moments of the Markovian random evolutions in two and four dimensions.
- A virtual analog of Pollaczek-Khintchin transform equation.
- Resolvability of some special algebras with topologies.
- Groups with many hypercentral subgroups.
- The Euler Tour of n-Dimensional Manifold with Positive Genus.
- Symmetric random evolution in the space ℜ6.
- On numerical algorithms for solving multidimensional analogs of the Kendall functional equation.
- Classification of Aff(2, ℜ)-orbit's dimensions for quadratic differential system.
- Professor Mihail Popa - 60th anniversary.
- Academician Radu Miron - Eighty Years of Life and Sixty Years of Efforts.
