Oscillatory Cortical Activity during Visual Hallucinations

Journal of Biological Physics

Volumn 23, Issue 1, 1997, Pages 21-66

  Tass, Peter ^a  

^a HEINRICH HEINE UNIVERSITY   (Germany)

Author keywords

Activator inhibitor network; Bifurcation; Blinking rolls; Center manifold; Order parameter equation; Pattern formation; Visual hallucinations

Indexed keywords

EID: 0003027876     PISSN: 00920606     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1004990707739     Document Type: Article

References (25)

1. Arnold, V.I.: Geometrical methods in the theory of ordinary differential equations, Springer, Berlin, Heidelberg, New York, 1983.
2. Bestehorn M., Friedrich R., Haken H.: Modulated traveling waves in nonequilibrium systems: the 'blinking state', Z. Phys. B 77 (1989), 151-155.
3. Coddington E.A., Levinson N.: Ordinary differential equations, McGraw-Hill, New York, 1955.
4. Cowan, J.D.: Some remarks on channel bandwidths for visual contrast detection, Neurosci. Res. Bull. 15 (1977), 492-515.
5. Cowan, J.D.: Brain mechanisms underlying visual hallucinations, in D. Paines (ed.), Emerging syntheses in science, Addison-Wesley, New York, 1987, pp. 123-131.
6. Ermentrout, G.B., Cowan, J.: A mathematical theory of visual hallucination patterns, Biol. Cybern. 34 (1979), 137-150.
7. Fineberg J., Moses E., Steinberg V.: Spatially and temporally modulated traveling-wave pattern in convecting binary mixtures, Phys. Rev. Lett. 61 (1988), 838-841.
8. Guckenheimer J., Holmes P.: Nonlinear oscillations, dynamical systems, and bifurcations of vector fields, Springer, Berlin, Heidelberg, New York, 1983.
9. Haken, H.: Synergetics: An introduction, Springer, Berlin, Heidelberg, New York, 1977.
10. Haken, H.: Advanced synergetics, Springer, Berlin, Heidelberg, New York, 1983.
11. Haken, H: Synergetic computers and cognition, Springer, Berlin, Heidelberg, New York, 1991.
12. Haken, H.: Principles of brain functioning: A synergetic approach to brain activity, behaviour and cognition, Springer, Berlin, Heidelberg, New York, 1995.
13. Hale, J.K.: Ordinary differential equations, Wiley, New York, 1969.
14. Horowitz M.J., Adams J.E., Rutkin B.B.: Evoked hallucinations in epilepsy, Psychiatr. Speculator 11 (1967), 4.
15. Kelley A.: The stable, center-stable, center, center-unstable and unstable manifolds, J. Diff. Equ. 3 (1967), 546-570.
16. Klüver, H.: Mescal and mechanisms of hallucination, University of Chicago Press, 1967.
17. Markus, M., Schepers, H.: Pattern formation in neural activator-inhibitor networks, in S.C. Müller, T. Plesser (eds.), Contributions to the Dortmunder Dynamische Woche June 1992, Projekt-Verlag, Dortmund, 1992.
18. Murray, J.D.: Mathematical biology, Springer, Berlin, Heidelberg, New York, 1989.
19. Pego R.L., Weinstein M.I.: Asymptotic stability of solitary waves, Comm. Math. Phys. 22 (1994), 1-50.
20. Pliss V.: Principal reduction in the theory of stability of motion, Izv. Akad. Nauk. SSSR Math. Ser. 28 (1964), 1297-1324.
21. Sattinger D.H.: On the stability of waves of nonlinear parabolic systems, Advances in Mathematics 22 (1976), 312-355.
22. Schwartz E.: Spatial mapping in the primate sensory projection: Analytic structure and relevance to perception, Biol. Cybernetics 25 (1977), 181-194.
23. Siegel R.K., West L.J. (eds.): Hallucinations, Wiley, New York, 1975.
24. Tass, P.: Cortical pattern formation during visual hallucinations, J. Biol. Phys. 21 (1995), 177-210.
25. Winfree, A.T.: The geometry of biological time, Springer, Berlin, Heidelberg, New York, 1980.