Mathematical Psychology and Psychophysiology

By Stephen Grossberg | Go to book overview
FIGURE 48. A flow on ∏0 with n + h ≡ constant, as in the FitzHugh-Nagumo equations.

straight lines (Figure 48). Also, UP(θ0) is the straight line whose equation is
n + hn0 + h0.

Thus, no solution in ∏0 starting at DOWN(θ0) ever crosses UP(θ0). There exist, therefore, Ω-periodic and single pulse solutions, but no burst or finite wave train solutions for small ε and δ. Recent work by Evans, Fenichel, and Feroe [ 1980] implies that if ε is sufficiently large, so that two of the eigenvalues at the rest point become complex conjugate, and if certain other hypotheses are satisfied, then there exist finite wave train solutions of the FitzHugh-Nagumo equations. Computations by Feroe [ 1980] for a piecewise-linear model and by Hastings [ 1980] for a model with cubic G-function indicate that the necessary hypotheses may be satisfied in certain parameter ranges. These Evans-Fenichel-Feroe wave trains have qualitative properties different from those discussed previously: the spikes are widely- and nearly evenly-spaced, with each spike an approximate copy of a single spike. They resemble a finite set of low-frequency Ω-periodic spikes.


REFERENCES

1. W. J. Adelman and R. FitzHugh, "Solutions of the Hodgkin-Huxley equations modified for potassium accumulation in a periaxonal space", Fed. Proc. 34 ( 1975), 1322-1329.

2. T. E. Anderson and L. T. Rutledge, "Inhibition in penicillin-induced epileptic foci", Electroenceph. Clin. Neurophysiol. 46 ( 1979), 498-509.

3. J. Atkinson and A. Ward, "Intracellular studies of cortical neurons in chronic epileptogenic foci in the monkey", Experimental Neurol. 10 ( 1964), 285-295.

4. H. Bade, H. A. Braun and H. Hensel, "Parameters of the static burst discharge of lingual cold receptors in the cat", Pflügers Arch. 382 ( 1979), 1-5.

5. J. L. Barker and T. G. Smith Jr., "Electrophysiological studies of molluscan neurons generating bursting pacemaker potential activity", Abnormal Neuronal Discharges, Raven Press, New York, 1978, pp. 359-387.

6. J. Bell and L. P. Cook, "On the solutions of a nerve conduction equation", SIAM J. Appl. Math. 35. ( 1978), 678-688.

-88-

Notes for this page

Add a new note
If you are trying to select text to create highlights or citations, remember that you must now click or tap on the first word, and then click or tap on the last word.
One moment ...
Default project is now your active project.
Project items

Items saved from this book

This book has been saved
Highlights (0)
Some of your highlights are legacy items.

Highlights saved before July 30, 2012 will not be displayed on their respective source pages.

You can easily re-create the highlights by opening the book page or article, selecting the text, and clicking “Highlight.”

Citations (0)
Some of your citations are legacy items.

Any citation created before July 30, 2012 will labeled as a “Cited page.” New citations will be saved as cited passages, pages or articles.

We also added the ability to view new citations from your projects or the book or article where you created them.

Notes (0)
Bookmarks (0)

You have no saved items from this book

Project items include:
  • Saved book/article
  • Highlights
  • Quotes/citations
  • Notes
  • Bookmarks
Notes
Cite this page

Cited page

Style
Citations are available only to our active members.
Sign up now to cite pages or passages in MLA, APA and Chicago citation styles.

(Einhorn, 1992, p. 25)

(Einhorn 25)

1

1. Lois J. Einhorn, Abraham Lincoln, the Orator: Penetrating the Lincoln Legend (Westport, CT: Greenwood Press, 1992), 25, http://www.questia.com/read/27419298.

Cited page

Bookmark this page
Mathematical Psychology and Psychophysiology
Table of contents

Table of contents

Settings

Settings

Typeface
Text size Smaller Larger Reset View mode
Search within

Search within this book

Look up

Look up a word

  • Dictionary
  • Thesaurus
Please submit a word or phrase above.
Print this page

Print this page

Why can't I print more than one page at a time?

Full screen
/ 320

matching results for page

Cited passage

Style
Citations are available only to our active members.
Sign up now to cite pages or passages in MLA, APA and Chicago citation styles.

"Portraying himself as an honest, ordinary person helped Lincoln identify with his audiences." (Einhorn, 1992, p. 25).

"Portraying himself as an honest, ordinary person helped Lincoln identify with his audiences." (Einhorn 25)

"Portraying himself as an honest, ordinary person helped Lincoln identify with his audiences."1

1. Lois J. Einhorn, Abraham Lincoln, the Orator: Penetrating the Lincoln Legend (Westport, CT: Greenwood Press, 1992), 25, http://www.questia.com/read/27419298.

Cited passage

Welcome to the new Questia Reader

The Questia Reader has been updated to provide you with an even better online reading experience.  It is now 100% Responsive, which means you can read our books and articles on any sized device you wish.  All of your favorite tools like notes, highlights, and citations are still here, but the way you select text has been updated to be easier to use, especially on touchscreen devices.  Here's how:

1. Click or tap the first word you want to select.
2. Click or tap the last word you want to select.

OK, got it!

Thanks for trying Questia!

Please continue trying out our research tools, but please note, full functionality is available only to our active members.

Your work will be lost once you leave this Web page.

For full access in an ad-free environment, sign up now for a FREE, 1-day trial.

Already a member? Log in now.