scholarly journals About Nonuniqueness of Solutions of the Showalter-Sidorov Problem for One Mathematical Model of Nerve Impulse Spread in Membrane

2018 ◽  
Vol 11 (4) ◽  
pp. 161-168
Author(s):  
N.А. Manakova ◽  
◽  
O.V. Gavrilova ◽  
Keyword(s):  
Mathematical Model ◽  
Nerve Impulse ◽  
Nonuniqueness Of Solutions

scholarly journals The study of chaotic and regular regimes of the fractal oscillators FitzHugh-Nagumo

2018 ◽  
Vol 62 ◽  
pp. 02017 ◽  
Author(s):  
Olga Lipko ◽  
Roman Parovik
Keyword(s):  
Mathematical Model ◽  
Lyapunov Exponents ◽  
Nerve Impulse ◽  
Chaotic Attractors ◽  
Control Parameters ◽  
Schmidt Orthogonalization ◽  
Non Local ◽  
Explicit Finite Difference ◽  
Maximum Lyapunov Exponents ◽  
Orthogonalization Procedure

In this paper we study the conditions for the existence of chaotic and regular oscillatory regimes of the hereditary oscillator FitzHugh-Nagumo (FHN), a mathematical model for the propagation of a nerve impulse in a membrane. To achieve this goal, using the non-local explicit finite-difference scheme and Wolf’s algorithm with the Gram-Schmidt orthogonalization procedure and the spectra of the maximum Lyapunov exponents were also constructed depending on the values of the control parameters of the model of the FHN. The results of the calculations showed that there are spectra of maximum Lyapunov exponents both with positive values and with negative values. The results of the calculations were also confirmed with the help of oscillograms and phase trajectories, which indicates the possibility of the existence of both chaotic attractors and limit cycles.

Evaluation of a mathematical model analysing the relation between intradental nerve impulse activity and perceived pain in man

1986 ◽  
Vol 19 (3-4) ◽  
pp. 261-277 ◽  
Author(s):  
Uno G.H. Fors ◽  
Michael L. Ahlquist ◽  
Lennart G.A. Edwall ◽  
Glenn A.T. Haegerstam
Keyword(s):  
Mathematical Model ◽  
Impulse Activity ◽  
Nerve Impulse ◽  
Perceived Pain

XRF and PIXE Analysis of light and Dark Adapted Ocular Tissue

1982 ◽  
Vol 40 ◽  
pp. 190-191
Author(s):  
B. J. Panessa ◽  
H. W. Kraner ◽  
J. B. Warren ◽  
K. W. Jones
Keyword(s):  
Trace Metals ◽  
Pigment Epithelium ◽  
Nerve Impulse ◽  
Light Response ◽  
Ocular Tissue ◽  
Emission Spectrometry ◽  
Retinol Dehydrogenase ◽  
Pixe Analysis ◽  
X Ray ◽  
Optimal Function

During photoexcitation the retina requires specific electrolytes and trace metals for optimal function (Na, Mg, Cl, K, Ca, S, P, Cu and Zn). According to Hagins (1981), photoexcitation and generation of a nerve impulse involves the movement of Ca from the rhodopsin-ladened membranes of the rod outer segment (ROS) to the plasmalemma, which in turn decreases the in-flow of Na into the photoreceptor, resulting in hyperpolarization. In toad isolated retinas, the presence of Ba has been found to increase the amplitude and prolong the delay of the light response (Brown and Flaming, 1978). Trace metals such as Cu, Zn and Se are essential for the activity of the metalloenzymes of the retina and retina pigment epithelium (RPE) (i.e. carbonic anhydrase, retinol dehydrogenase, tyrosinase, glutathione peroxidase, superoxide dismutase...). Therefore the content and fluctuations of these elements in the retina and choroid are of fundamental importance for the maintenance of vision. This paper presents elemental data from light and dark adapted frog ocular tissues examined by electron beam induced x-ray microanalysis, x-ray fluorescence spectrometry (XRF) and proton induced x-ray emission spectrometry (PIXE).

Mathematical model of hit phenomena and its application to movie advertisement

2008 ◽  
Author(s):  
Ishii Akira ◽  
Yoshida Narihiko ◽  
Hayashi Takafumi ◽  
Umemura Sanae ◽  
Nakagawa Takeshi
Keyword(s):  
Mathematical Model
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