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Dynamics of the olfactory bulb: bifurcations, learning, and memory

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Abstract

A mathematical model for describing dynamic phenomena in the olfactory bulb is presented. The nature of attractors and the bifurcation sequences in terms of the lateral connection strength in the mitral layer are studied numerically. Chaotic activity has only been found in the case of strong excitatory coupling. Synaptic modification-induced transition from oscillation to chaos is demonstrated. A model for a simple associative memory is also presented.

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References

  • Adrian ED (1950) The electrical activity of the mammalian olfactory bulb. Electroencephalogr Clin Neurophysiol 2:377–388

    Google Scholar 

  • Ambros-Ingerson L, Granger R, Lynch G (1990) Simulation of paleocortex performs hierarchical clustering. Science 247:1344–1348

    Google Scholar 

  • Baird B (1986) Non-linear dynamics of pattern formation and pattern recognition in the rabbit olfactory bulb. Physica 22D:150–179

    Google Scholar 

  • Baird B (1990) Bifurcation and category learning in network models of oscillating cortex. Physica 42D:365–384

    Google Scholar 

  • Barnard E (1989) Analysis of the Lynch-Granger model for olfactory cortex. Biol Cybern 62:151–155

    Google Scholar 

  • Brennan P, Keverne EB (1989) Impairment of olfactory memory by local infusions of non-selective excitatory amino acid receptor antagonists into the accessory olfactory bulb. Neuroscience 33:463–468

    Google Scholar 

  • Brennan P, Kaba H, Keverne EB (1990) Olfactory recognition: a simple memory system. Science 250:1223–1226

    Google Scholar 

  • Borisyuk RM, Kirillov AB (1992) Bifurcation analysis of a neural network model. Biol Cybern 66:319–325

    Google Scholar 

  • Bressler SL (1987a) Relation of olfactory bulb and cortex. I. Spatial variation of bulbo-cortical interdependence. Brain Res 409:285–293

    Google Scholar 

  • Bressler SL (1987b) Relation of olfactory bulb and cortex. II. Model for driving of cortex by bulb. Brain Res 409:294–301

    Google Scholar 

  • Érdi P, Grőbler T, Kaski K (1992) Dynamic phenomena in the olfactory bulb. I. Bifurcation sequences, coexistence of periodicity and chaos, synaptic modification induced transitions. In: Aleksander I, Taylor J (eds) Artificial neural networks 2. North-Holland, Amsterdam, pp 873–876

    Google Scholar 

  • Freeman WJ (1975) Mass action in the nervous system. Academic Press, New York

    Google Scholar 

  • Freeman WJ (1978) Spatial properties of an EEG event in the olfactory bulb and cortex. Electroencephalogr Clin Neurophysiol 44:585–605

    Google Scholar 

  • Freeman WJ (1979) Nonlinear gain mediating cortical stimulus-response relations. Biol Cybern 33:237–247

    Google Scholar 

  • Freeman WJ, Schneider W (1982) Changes in spatial patterns of rabbit olfactory EEG with conditioning to odours. Psychophysiology 19:44–56

    Google Scholar 

  • Freeman WJ, Skarda C (1985) Spatial EEG patterns, non-linear dynamics and perception: the neo-Sherringtonian view. Brain Res Rev 10:147–175

    Google Scholar 

  • Frouzakis CE, Adomaltis RA, Kevrekidis IG (1991) Resonance phenomena in an adaptively controlled system. Int J Bifurcation Chaos 1:83

    Google Scholar 

  • Granger R, Ambros-Ingerson J, Lynch G (1989) Derivation of encoding characteristics of layer II cerebral cortex. J Cog Neurosci 1:61–87

    Google Scholar 

  • Grőbler T, Érdi P, Kaski K (1992) Dynamic phenomena in the olfactory bulb. II. Model for a simple associative memory. In: Aleksander I, Taylor J (eds) Artificial neural networks 2. North-Holland, pp 877–880

  • Halász N (1990) The vertebrate olfactory system. Akadémiai Kiadó, Budapest

    Google Scholar 

  • Hebb DO (1949) The organization of behaviour. Wiley, New York

    Google Scholar 

  • Holley A (1991) Neural coding of olfactory information. In: Getchell TV et al (eds) Smell and taste in health and disease. Raven Press, New York, pp 329–343

    Google Scholar 

  • Hopfield JJ (1991) Olfactory computation and object perception. Proc Natl Acad Sci USA 88:6462–6466

    Google Scholar 

  • Hudson R, Distel H (1987) Regional autonomy in the peripheral processing of odour signals in newborn rabbits. Brain Res 421:85–94

    Google Scholar 

  • Hudson R, Distel H, Zippel P (1990) Perceptual performance in peripherically reduced olfactory systems. In: Schild D (eds) Chemosensory information processing. Springer, Berlin Heidelberg New York, pp 259–279

    Google Scholar 

  • Keener (1981) Infinite period bifurcation and global bifurcation branches. SIAM J Appl Math 41:127–144

    Google Scholar 

  • Li Z (1990) A model of olfactory adaptation and sensitivity enhancement in the olfactory bulb. Biol Cybern 62:349–361

    Google Scholar 

  • Li Z, Hopfield JJ (1989) Modelling the olfactory bulb and its neural oscillatory processings. Biol Cybern 61:379–392

    Google Scholar 

  • Liljenström H (1991) Modelling the dynamics of olfactory cortex using simplified network units and realistic architecture. Int J Neural Systems 2:1–15

    Google Scholar 

  • Riedel H, Schild D (1992) The dynamics of Hebbian synapses can be stabilized by a nonlinear decay term. Neural Networks 5:454–463

    Google Scholar 

  • Schild D (1988) Principles of odour coding and a neural network for odour discrimination. Biophys J 54:1001–1011

    Google Scholar 

  • Schild D (1990) Chemosensory information processing. (NATA ASI Series vol H 39) Springer, Berlin Heidelberg New York

    Google Scholar 

  • Schild D, Riedel H (1992) The significance of glomerular compartmentalization for olfactory coding. Biophys J 61:704–715

    Google Scholar 

  • Scott JW (1991) Central processing of olfaction. J Steroid Biochem Biol 39:593–600

    Google Scholar 

  • Scott JW, Harrison TA (1987) The olfactory bulb: anatomy and physiology. In: Finger TE, Silver WL (eds) Neurobiology of taste and smell. Wiley, New York

    Google Scholar 

  • Shepherd GM, Greer CA (1990) Olfactory bulb. In: Shepherd GM (eds) The synaptic organization of the brain. Oxford University Press, New York, pp 133–169

    Google Scholar 

  • Skarda C, Freeman WJ (1987) How brains make chaos in order to make sense of the world. Behav Brain Sci 10:161–195

    Google Scholar 

  • Taylor JG, Keverne BE (1991) Accessory olfactory learning. Biol Cybern 64:301–305

    Google Scholar 

  • Trombley PO, Shepherd GM (1991) Norepinephrine inhibits mitral ell evoked EPSPs in mammalian olfactory bulb granule cells in culture. Soc Neurosci Abstr 17:103–12

    Google Scholar 

  • Willey TJ (1973) The ultrastructure of the cat olfactory bulb. J Comp Neurol 152:211–232

    Google Scholar 

  • Wilson MA, Bower JM (1992) Cortical oscillations and temporal interactions in a computer simulation of piriform cortex. J Neurophysiol 67:981–995

    Google Scholar 

  • Yao Y, Freeman WJ (1990) Model of biological pattern recognition with spatially chaotic dynamics. Neural Networks 3:153–170

    Google Scholar 

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Authors and Affiliations

  1. Biophysics Group, KFKI Research Institute for Particle and Nuclear Physics of the Hungarian Academy of Sciences, P.O. Box 49, H-1525, Budapest, Hungary

    P. Érdi, T. Grőbler & G. Barna

  2. Tampere University of Technology, Microelectronics Laboratory, P.O. Box 527, SF-33101, Tampere, Finland

    P. Érdi, T. Grőbler & K. Kaski

  3. Department of Artificial Intelligence, Kyushu Institute of Technology, Iizuka 820, Fukuoka, Japan

    G. Barna

Authors
  1. P. Érdi
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  2. T. Grőbler
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  3. G. Barna
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  4. K. Kaski
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Érdi, P., Grőbler, T., Barna, G. et al. Dynamics of the olfactory bulb: bifurcations, learning, and memory. Biol. Cybern. 69, 57–66 (1993). https://doi.org/10.1007/BF00201408

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  • DOI: https://doi.org/10.1007/BF00201408

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