Low-Dimensional Chaos in a Simple Biological Model of Neocortex

Implications for Cardiovascular and Cognitive Disorders
  • James E. Skinner
  • Mirna Mitra
  • Keith Fulton
Part of the The Springer Series in Behavioral Psychophysiology and Medicine book series (SSBP)


Our laboratory has been interested in understanding the neural mechanisms involved in information processing in neocortex, especially in those structures that regulate the sensory and cardiovascular systems. Studies in comparative physiology suggest a theoretical basis for the regulation of the cardiovascular system by the brain. Following his life’s work, Cannon (1931) hypothesized the existence of a cerebral mechanism in which sensory input and autonomic output were simultaneously orchestrated; this orchestration, he suggested, became a focus for natural selection and evolved to enable the higher mammal to attend to its environment and simultaneously to prepare autonomic support in anticipation of the occurrence of certain survival behaviors that might be released.


Olfactory Bulb Correlation Dimension Autonomic Support Cognitive Disorder Mitral Cell 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. Babloyantz, A., & Destexhe, A. (1986). Low-dimensional chaos in an instance of epilepsy. Proceedings of the National Academy of Sciences of the USA, 83, 3513–3517.PubMedCrossRefGoogle Scholar
  2. Babloyantz, A., & Destexhe, A. (1987). Strange attractors in the human cortex. In L. Rensing, U. van der Heiden, & M. C. Mackey (Eds.), Temporal disorder in human oscillatory systems. Springer Series in Synergetics (Vol. 36, pp. 488–456). Berlin: Springer-Verlag.Google Scholar
  3. Bak, P. (1985). Mode-locking and the transition to chaos in dissipative systems. Physica Scripta, T9, 50–58.CrossRefGoogle Scholar
  4. Bak, P. (1986). The devil’s staircase. Physics Today, 86, 38–45.CrossRefGoogle Scholar
  5. Barnsley, M. F., & Sloan, A. D. (1988). A better way to compress images. Byte, 1, 215–223.Google Scholar
  6. Barnsley, M. F., Massopust, P., Strickland, H., & Sloan, A. D. (1987). Fractal modeling of biological structures. Annals of New York Academy of Sciences, 504, 179–194.CrossRefGoogle Scholar
  7. Bliss, T. V. P., Goddard, G. V., & Rives, M. (1983). Reduction of long-term potentiation in the dentate gyrus of the rat following selective depletion of monoamines. Journal of Physiology (London), 334, 475–491.Google Scholar
  8. Bullock, T. H., & Basar, E. (1988). Comparison of ongoing compound field potentials in the brains of invertebrates and vertebrates. Brain Research, 472, 57–75.PubMedGoogle Scholar
  9. Cannon, W. B. (1931). Again the James-Lange and the thalamic theories of emotion. Psychological Review, 38, 281–295.CrossRefGoogle Scholar
  10. Chay, T. R., & Rinzel, J. (1985). Bursting, beating, and chaos in an excitable membrane model. Biophysical Journal, 47, 357–366.PubMedCrossRefGoogle Scholar
  11. Farmer, J. D. (1982). Dimension, fractal, measures, and chaotic dynamics. In H. Haken (Ed.), Evolution of order and chaos. Heidelberg: Springer-Verlag.Google Scholar
  12. Folkow, B. (1982). Physiological aspects of primary hypertension. Physiological Reviews, 62, 347–504.PubMedGoogle Scholar
  13. Freeman, W. J., & Schneider, W. S. (1982). Changes in spatial patterns of rabbit olfactory EEG with conditioning to odors. Psychophysiology, 19, 44–56.PubMedCrossRefGoogle Scholar
  14. Gleick, J. (1987). Chaos: Making a new science. New York: Viking Penguin.Google Scholar
  15. Graf, K. E., & Elbert, T. (1989). Dimensional analysis of the waking EEG. In E. Basar & T. H. Bullock (Ed.), Brain Dynamics Progress and Perspectives (pp. 174–191). Berlin: Springer-Verlag.CrossRefGoogle Scholar
  16. Grassberger, P., & Procaccia, I. (1983). Measuring the strangeness of strange attractors. Physica 9D, 183–208.Google Scholar
  17. Gray, C. M., & Skinner, J. E. (1988). Centrifugal regulation of neuronal activity in the olfactory bulb of the waking rabbit as revealed by reversible cryogenic blockade. Experimental Brain Research, 69, 378–386.CrossRefGoogle Scholar
  18. Gray, C. M., Freeman, W. J., & Skinner, J. E. (1984). Associative changes in the spatial amplitude patterns of rabbit olfactory EEG are norepinephrine-dependent. Society for Neuroscience Abstracts, 10, 121.Google Scholar
  19. Gray, C. M., Freeman, W. J., & Skinner, J. E. (1986). Chemical dependencies of learning in the rabbit olfactory bulb: Acquisition of the transient spatial pattern change depends on norepinephrine. Behavioral Neuroscience, 100, 585–596.PubMedCrossRefGoogle Scholar
  20. Hess, B., & Markus, M. (1987). Order and chaos in biochemistry. Trends in Biochemical Science, 12, 45–48.CrossRefGoogle Scholar
  21. Hildebrandt, J. D., Sekura, R. D., Codina, J., Iyengar, R., Manclark, C. R., & Birnbaumer, L. (1983). Stimulation and inhibition of adenylyl cyclases is mediated by distinct proteins. Nature, 302, 706–709.PubMedCrossRefGoogle Scholar
  22. Hopfield, J. J., & Tank, D. W. (1986). Computing with neural circuits: A model. Science, 233, 626–633.CrossRefGoogle Scholar
  23. Hopkins, W. F., & Johnston, D. (1984). Frequency-dependent noradrenergic modulation of long-term potentiation in the hippocampus. Science, 226, 350–352.PubMedCrossRefGoogle Scholar
  24. Hopkins, W. F., & Johnston, D. (1988). Noradrenergic enhancement of long-term potentiation at mossy fiber synapses in the hippocampus. Journal of Neurophysiology, 59, 667–687.PubMedGoogle Scholar
  25. Krontiris-Litowitz, J., Skinner, J. E., & Birnbaumer, L. (1985). A muscarinic agonist (Ethmozine) prevents long-term potentiation in the hippocampal slice. Society for Neuroscience Abstracts, 11,781.Google Scholar
  26. Levitt, P., & Noebels, J. L. (1981). Mutant mouse tottering: Selective increase of locus ceruleus axons in a defined single-locus mutation. Proceedings of the National Academy of Sciences of the USA, 78, 4630–4634.PubMedCrossRefGoogle Scholar
  27. Liebovitch, L. S., & Sullivan, M. J. (1987). Fractal analysis of a voltage-dependent potassium channel from cultured mouse hippocampal neurons. Biophysical Journal, 52, 979–988.PubMedCrossRefGoogle Scholar
  28. Liebovitch, L. S., Fischbarg, J., Koniarek, J. P., Todorova, I., & Wang, M. (1987). Fractal model of ion-channel kinetics. Biochimica et Biophysica Acta, 896, 173–180.PubMedCrossRefGoogle Scholar
  29. Mandelbrot, B. B. (1983). The fractal geometry of nature. New York: W. H. Freeman.Google Scholar
  30. Markus, M., Kuschmitz, E., & Hess, B. (1985). Properties of strange attractors in yeast glycolysis. Biophysical Chemistry, 22, 95–105.PubMedCrossRefGoogle Scholar
  31. Mayer-Kress, G. (1986). Introductory remarks. In G. Mayer-Kress (Ed.), Dimensions and entropies in chaotic systems (pp. 2–5). New York: Springer-Verlag.CrossRefGoogle Scholar
  32. Neurotech. (1988). Supporting data for the “Stress Analyzer.” Neurotech Laboratories, Inc., Suite 340, 1120 Medical Plaza, The Woodlands, Texas 77380.Google Scholar
  33. Packard, N. H., Crutchfield, J. P., Farmer, J. D., & Shaw, R. S. (1980). Geometry from a time-series. Physical Review Letters, 45, 712.CrossRefGoogle Scholar
  34. Reid, J. L., Lewis, P. J., Myers, M. G., & Dollery, C. T. (1974). Cardiovascular effects of intracerebroventricular d-, 1-, and dl-propranolol in the conscious rabbit. Journal of Pharmacology and Experimental Therapeutics, 188, 391–399.Google Scholar
  35. Roschke, J., & Basar, E. (1989). Correlation dimensions in various parts of cat and human brain in different states. In E. Basar & T. H. Bullock (Eds.), Brain dynamics progress and perspectives (pp. 131–148). Berlin: Springer-Verlag.CrossRefGoogle Scholar
  36. Sejnowski, T. J., & Rosenberg, C. R. (1987). Parallel networks that learn to pronounce English text. Complex Systems 1, 145–168.Google Scholar
  37. Shepherd, G. M. (1970). The olfactory bulb as a simple cortical system: Experimental analysis and functional implications. In F. O. Schmitt (Ed.), The neurosciences: Second study program (pp. 539–552). New York: Rockefeller University Press.Google Scholar
  38. Skarda, C. A., & Freeman, W. J. (1987). How brains make chaos in order to make sense of the world. Behavioral and Brain Sciences, 10, 161–173.CrossRefGoogle Scholar
  39. Skinner, J. E. (1971). Abolition of a conditioned, surface-negative, cortical potential during cryogenic blockade of the nonspecific thalamo-cortical system. Electroencephalography and Clinical Neurophysiology, 31, 197–209.PubMedCrossRefGoogle Scholar
  40. Skinner, J. E. (1984). Central gating mechanisms that regulate event-related potentials and behavior. In T. Elbert, B. Rockstroh, W. Lutzenberger, & N. Birbaumer (Eds.), Self-regulation of the brain and behavior (pp. 42–58). New York: Springer-Verlag.CrossRefGoogle Scholar
  41. Skinner, J. E. (1988). Brain involvement in cardiovascular disorders. In T. Elbert, W. Langosch, A. Steptoe, & D. Vaitl (Eds.), Behavioural medicine in cardiovascular disorders (pp. 229–253). London: Wiley.Google Scholar
  42. Skinner, J. E., & King G. L. (1980). Contribution of neuron dendrites to extracellular sustained potential shifts. In H. H. Kornhuber & L. Deecke (Eds.), Motivation motor and sensory processes of the brain. Progress in brain research (Vol. 54, pp. 89–102. Amsterdam: Elsevier/North-Holland Biomedical Press.Google Scholar
  43. Skinner, J. E., & Molnar, M. (1983). Event-related extracellular potassium-ion activity changes in the frontal cortex of the conscious cat. Journal of Neurophysiology, 49, 204–215.PubMedGoogle Scholar
  44. Skinner, J. E., & Pratt, C. M. (1982). Ethmozin reduces the amplitude of the cerebral event-related slow potential in patients with ischemic heart disease. Abstracts of the American Heart Association.Google Scholar
  45. Skinner, J. E., & Reed, J. C. (1981). Blockade of a frontocortical-brainstem pathway prevents ventricular fibrillation of the ischemic heart in pigs. American Journal of Physiology, 240, H1156–H163.Google Scholar
  46. Skinner, J. E., & Yingling, C. D. (1976). Regulation of slow potential shifts in nucleus reticularis thalami by the mesencephalic reticular formation and the frontal cortex. Electroencephalography and Clinical Neurophysiology, 40, 288–296.PubMedCrossRefGoogle Scholar
  47. Skinner, J. E., & Yingling, C. D. (1977). Central gating mechanisms that regulate event-related potentials and behavior: A neural model for attention. In J. E. Desmedt (Ed.), Progress in clinical neurophysiology (Vol. 1, pp. 30–69). Brussels: Karger-Basel.Google Scholar
  48. Skinner, J. E., Reed, J. C., Welch, K. M. A., & Nell, J. H. (1978). Cutaneous shock produces correlated shifts in slow potential amplitude and cyclic 3′, 5′-adenosine monophos-phate level in the parietal cortex of the conscious rat. Journal of Neurochemistry, 30, 699–704.PubMedCrossRefGoogle Scholar
  49. Skinner, J. E., Martin, J. L., Landisman, C. E., Mommer, M. M., Fulton, K., Mitra, M., Burton, W. D., & Saltzberg, B. (1988). Chaotic attractors in a model of neocortex: Dimensionalities of olfactory bulb surface potentials are spatially uniform and event-related. In E. Basar & T. H. Bullock (Eds.), Brain dynamics progress and perspectives (pp. 168–173). Dynamics of sensory and cognitive processing by the brain. Berlin: Springer-Verlag.Google Scholar
  50. Steptoe, A. (1988). The processes underlying long-term blood pressure reductions in essential hypertensives following behavioural therapy. In T. Elbert, W. Langosch, A. Steptoe, & D. Vaitl (Eds.), Behavioural medicine in cardiovascular disorders (pp. 139–148). London: Wiley.Google Scholar
  51. Szilagyi, J. E., Taylor, A. A., & Skinner, J. E. (1987). Cryoblockade of the ventromedial frontal cortex reverses hypertension in the rat. Hypertension, 9, 576–581.PubMedCrossRefGoogle Scholar
  52. Tackett, R. L., Webb, J. G., & Privitera, P. J. (1985). Site and mechanism of the centrally mediated hypotensive action of propranolol. Journal of Pharmacology and Experimental Therapeutics, 235, 66–70.PubMedGoogle Scholar
  53. Takens, F. (1981). Detecting strange attractors in turbulence. In Warwick (Ed.), Dynamical systems and Turbulence, 1980, Vol. 898 of Lecture Notes in Mathematics. Berlin: Springer-Verlag.Google Scholar
  54. Theiler, J. (1986). Spurious dimension from correlation algorithms applied to limited time-series data. Physical Review A, 34, 2427–2432.PubMedCrossRefGoogle Scholar
  55. Theiler, J. (1988). Quantifying chaos: Practical estimation of the correlation dimension. Doctoral dissertation, California Institute of Technology, Pasadena.Google Scholar
  56. Thompson, J. W., Newton, P., Pocock, P. V., Cooper, R., Crow, H., McCallum, W. C., & Papakostopoulos, D. (1978). Preliminary study of pharmacology of contingent negative variation in man. In D. A. Otto (Ed.), Multidisciplinary perspectives in event-related brain potential research (pp. 25–55). Washington, DC: U.S. Environmental Protection Agency.Google Scholar
  57. Watanabe, A. M., McConnaughey, M. M., Strawbridge, R. A., Fleming, J. W., Jones, L. R., & Besch, H. R., Jr. (1978). Muscarinic cholinergic receptor modulation of B-adrenergic receptor affinity for catecholamines. Journal of Biological Chemistry, 253, 4833–4836.PubMedGoogle Scholar
  58. Williams, S. H., & Johnston, D. (1988a). Muscarin depresses an APV-sensitive form of LTP in CA3 hippocampal neurons. Abstracts Society for Neuroscience, 14, p. 564.Google Scholar
  59. Williams, S. H., & Johnston, D. (1988b). Muscarinic depression of long-term potentiation in CA3 hippocampal neurons. Science, 242, 84–87.PubMedCrossRefGoogle Scholar
  60. Wilson, D. A., & Leon, M. (1988). Spatial patterns of olfactory bulb single-unit responses to learned olfactory cues in young rats. Journal of Neurophysiology, 59, 1770–1782.PubMedGoogle Scholar
  61. Wilson, D. A., Sullivan, R. M., & Leon, M. (1987). Single-unit analysis of postnatal olfactory learning: Modified olfactory bulb output response patterns to learned attractive odors. Journal of Neuroscience, 7, 3154–3162.PubMedGoogle Scholar
  62. Yingling, C. D., & Skinner, J. E. (1976). Selective regulation of thalamic sensory relay nuclei by nucleus reticularis thalami. Electroencephalography and Clinical Neurophysiology, 41, 476–482.PubMedCrossRefGoogle Scholar
  63. Yingling, C. D., & Skinner, J. E. (1977). Gating of thalamic input to cerebral cortex by nucleus reticularis thalami. In J. E. Desmedt (Ed.), Progress in clinical neurophysiology (Vol. 1, pp. 70–96). Brussels: Karger-Basel.Google Scholar

Copyright information

© Springer Science+Business Media New York 1991

Authors and Affiliations

  • James E. Skinner
    • 1
  • Mirna Mitra
    • 1
  • Keith Fulton
    • 1
  1. 1.Department of Neurology and Neuroscience ProgramBaylor College of MedicineHoustonUSA

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