Simulating Gamma Waveforms, AM Patterns and 1/fα Spectra by Means of Mesoscopic Chaotic Neurodynamics
Piecewise linear analysis modeled gamma activity as the output of an adaptive filter with white noise input (Elul 1972). Under this model a point attractor was postulated to govern the dynamics of the olfactory system under noise, which accounted for the broad spectrum of its background activity in the gamma range, the Gaussian amplitude density distribution, and the Rayleigh distribution of the peak amplitudes of the oscillations (Figure 3.13, c, p. 148 in Freeman 1975), but which failed to account for the 1/fα power spectral density and the spatial patterns of phase cones (Figure I in Prologue, Sections B and C). The gamma burst on inhalation was thought to be governed by a Hopf bifurcation to a limit cycle attractor. The amplitude and frequency modulations of bursts were ascribed to the brief time of access during inhalation, which allowed for an approach to the attractor, but with the next bifurcation coming too quickly to allow the state to settle into a stable orbit.
KeywordsOlfactory Bulb Chaotic Attractor Olfactory System Point Attractor Anterior Olfactory Nucleus
Unable to display preview. Download preview PDF.
- Abraham RI, Shaw CD (1983, 1985) Dynamics, the geometry of behavior. Ariel Press, Santa Cruz, CA, pp 220 (part 1), pp 137 (part 2), pp 121 (part 3)Google Scholar
- Conrad M (1986) What is the use of chaos? In: Holden A V (ed) Chaos. Manchester University Press, Manchester UK, pp 3–14Google Scholar
- Freeman WJ (1975) Mass action in the nervous system. Chap. 7. Academic Press, New York, p 489Google Scholar
- Freeman WJ (1985) Techniques used in the search for physiological basis for the EEG. In: Gevins A, Remond A (eds) Handbook of electroencephalography and clinical neurophysiology, vol 3A, part 2, chap 18. Elsevier, AmsterdamGoogle Scholar
- Freeman WJ, Viana Di Prisco G (1986) EEG spatial pattern: Palm G, Aertsen A (eds) Brain theory. Springer, Berlin Heidelberg New YorkGoogle Scholar
- Garfinkel A (1983) A mathematics for physiology. Am J Physiol 245: (Regul. Integr. Comp. Physiol., 14, R445–R446)Google Scholar
- Rössler OE (1983) The chaotic hierarchy. Z Naturforsch 38a: 788–801Google Scholar
- Schuster HG (1984) Deterministic chaos. Physik, Weinheim, p 220Google Scholar
- Shaw R (1984) The dripping faucet as a model chaotic system. Aerial Press, Santa Cruz CA, p 113Google Scholar
- Shepherd GM (1972) Synaptic organization of the mammalian olfactory bulb. Physiol Rev 52: 864–917Google Scholar