Some properties of a simplified nerve equation

Yoshizawa, Shuji; Kitada, Yasuhiko

doi:10.1016/0025-5564(69)90056-x

Cited by 5 publications

(2 citation statements)

References 2 publications

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“…Other quantities show similar behaviour. Yoshizawa (1969) has presented unsteady temperature profiles generated with a testparticle Monte Carlo scheme for a similar problem (Kn, = 0.5, x = 4).…”

Section: Table 1 Summarizes the Basic Simulation Conditions (Nominal mentioning

confidence: 99%

Transient motion of a confined rarefied gas due to wall heating or cooling

1993

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The transient motion that arises in a confined rarefied gas as a container wall is rapidly heated or cooled is simulated numerically. The Knudsen number based on nominal gas density and characteristic container dimension is varied from near-continuum to highly rarefied conditions. Solutions are generated with the direct simulation Monte Carlo method. Comparisons are made with finite-difference solutions of the Navier–Stokes equations, the limiting free-molecular values, and (continuum) results based on a small perturbation analysis. The wall heating and cooling scenarios considered induce relatively large acoustic disturbances in the gas, with characteristic flow speeds on the order of 20% of the local sound speed. Steady-state conditions are reached after on the order of 5 to 10 acoustic time units, here based on the initial speed of sound in the gas and the container dimension. As rarefaction increases, the initial gas response time is decreased. For the case of a rapid increase in wall temperature, transient rarefaction effects near the wall greatly alter gas response compared to the continuum predictions, even at relatively small nominal Knudsen number. For wall cooling, the continuum solution agrees well with direct simulation at that same Knudsen number. A local Knudsen number, based on the mean free path and the scale length of the temperature gradient, is found to be a more suitable indicator of transient rarefaction effects.

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Section: Table 1 Summarizes the Basic Simulation Conditions (Nominal mentioning

confidence: 99%

Transient motion of a confined rarefied gas due to wall heating or cooling

1993

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“…In our analysis we are essentially assuming an infinitely long axon. Numerical evidence 3,[15][16][17] shows that cubic and quadratic nonlinearities in F(V) are reasonably adequate forms. In particular, we choose the cubic form 4…”

Section: Introductionmentioning

confidence: 99%

Bifurcation analysis of the travelling waveform of FitzHugh–Nagumo nerve conduction model equation

Muruganandam

Lakshmanan

1997

Chaos: An Interdisciplinary Journal of Nonlinear Science

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The FitzHugh-Nagumo model for travelling wave type neuron excitation is studied in detail. Carrying out a linear stability analysis near the equilibrium point, we bring out various interesting bifurcations which the system admits when a specific Z(2) symmetry is present and when it is not. Based on a center manifold reduction and normal form analysis, the Hopf normal form is deduced. The condition for the onset of limit cycle oscillations is found to agree well with the numerical results. We further demonstrate numerically that the system admits a period doubling route to chaos both in the presence as well as in the absence of constant external stimuli. (c) 1997 American Institute of Physics.

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Stability properties of a model of parallel nerve fibers

Bell

Cosner

1981

Journal of Differential Equations

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Some properties of a simplified nerve equation

Cited by 5 publications

References 2 publications

Transient motion of a confined rarefied gas due to wall heating or cooling

Transient motion of a confined rarefied gas due to wall heating or cooling

Bifurcation analysis of the travelling waveform of FitzHugh–Nagumo nerve conduction model equation

Stability properties of a model of parallel nerve fibers

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