Skip to main content

Pattern Formation in Neural Systems I. Autorhytmicity, entrainment, quasiperiodicity and chaos in neurochemical systems

  • Chapter
Cybernetics and Systems ’86
  • 31 Accesses

Abstract

The skeleton model of transmitter recycling hypothesis describes rhytmic neurochemical behaviour due to the integrated synaptic activity. Interaction among neurochemical oscillators are modeled by a periodically perturbed nonlinear oscillator. Complex arrhytmic dynamics oocuring as transient phenomena might have connected with neurological disorders: synaptic level rhytmic generator requires a fine-tuned neurochemical control system.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • Barker, L. A. & Mittag J. W.: Comparative studies of substrates and inhibitors of choline transport and choline acetyl transferase. J.Pharmac.exp.Ther. 192 (86–94)1975

    Google Scholar 

  • Decroly, O. & Goldbeter, A: Birhytmicity, chaos, and other patterns of temporal selforganization in a multiply regulated biochemical system. Proc.Nat I.Acad.Sci.USA 79 (6917–6921)1982

    Article  Google Scholar 

  • Decroly, O. & Goldbeter, A.: Multiple periodic regime and final state sensitivity in a biochemical system. Phys. Lett. 105A (259–262)1984

    Google Scholar 

  • Dunant, Y., Israel, M., Lesbats, B. Manaranche, R.: Osci11ation of acetylcholine during nerve activity in the Torpado electric organ. Brain Res. 125(123–140)1977

    Article  Google Scholar 

  • Érdi, P.: Hierarchical thermodynamic approach to the brain. Int. J. Neurosei. 20 (193–216) 1983

    Article  Google Scholar 

  • Érdi, P & Tóth, J.: Osei11atorv phenomena at the synapse, Adv. Physiol. Sci. 34 (113–121)1981

    Google Scholar 

  • Fatt, P. & Katz, B.: Spontaneous subthreshold activity at motor nerve endings. J. Physiol. (London) 117 (109–128)1952

    Google Scholar 

  • Fritzsche, B. : Das Übertragungsverhaiten der neuromuskularen Synapse: Deutung experimentel1er Befunde durch ein Modell. Biol. Cybernetics 51 (335–346)1985

    Article  Google Scholar 

  • Gibson, G. E. Blass, J.: Inhibition of acetylcholine synthesis and of carbohydrate utilization by maple-syrupurine disease metabolites. J. Neurochem. 26 (1073–1078)1976a

    Article  Google Scholar 

  • Gibson, G. E. & Blass, J.: Impaired synthesis of acetylcholine in the brain accompanying mild hypoxia and hypoglycemia. J. Neurochem. 27 (37–42) 1976b

    Article  Google Scholar 

  • Goldbeter, A. & Decroly, O.: Temporal self-organization in biochemical systems:periodic behavior vs. chaos. Am. J. Physiol. 245 (R478–R483)1983

    Google Scholar 

  • Gottwald, B. A. & Wanner, G.: A reliable Rosenbrock Integrator for stiff differential equations. Computing 26 (355–360)1981

    Article  MathSciNet  Google Scholar 

  • Guevara, M. R., Glass, L. ,Mackey, C. & Shrier, A.: Chaos in neuorobioiogy. IEEE Trans. Systems, Man, and Cybernetics. SMC-13 (790–797)1983

    MATH  Google Scholar 

  • Holden, A. M. Muhamed, M. A.: Chaotic activity in neural systems. Cybernetic and System Research 2, Trappi, R. (ed) ( North-Holland, Amsterdam, 1984 ) pp. 245–250.

    Google Scholar 

  • Iooss, G, & Joseph,D. D.: Elementary Stability and Bifurcation Theory. Springer, New York-Heidelberg-Ber1in (1980)

    MATH  Google Scholar 

  • Israel, H., Lesbats, B., Manaranche, R.,.Marsal, J. &. Mastour-Frachon, P.: Related changes in amounts of ACh and ATP in resting and active torpedo nerve electrolaque synapse. J. Neurochem. 28 (1259–1267) 1977

    Google Scholar 

  • Jope, R. S.:High affinity choline transport and acetyl CoA production in brain and their roles in the regulation of acetylcholine synthesis. Brain. Res. Rev. (313–344) 1979

    Google Scholar 

  • Kai, T. & Tomita, K.: Stroboscopic phase portrait of a forced nonlinear oscillator. Prog. Theor. Phys. 61 (54–73),1979

    Article  Google Scholar 

  • Kantz, H. & Grassberger, P.: Repellers, semi-attractors, and long-lived chaotic transients. Physica 170(75–86)1935

    MathSciNet  Google Scholar 

  • Kaufmann, K.: On the kinetics of acetylcholine at the synapse. Naturwissenschaften 61 (371–376)1977

    Article  Google Scholar 

  • Kostova, T. V. & Markov, S. M. : A model of synaptic transmission. In: Dynamic phenomena in neurochemistry and neurophysics:theoretical aspects (Erdi, P. ed.) Budapest, 1985, pp. 44–51. of a model for transmitter

    Google Scholar 

  • Markus, M., Müller, S. C. Hess, B.: Observation of entrainment, quasiperiodicity and chaos in glycolyzinq yeast extracts under periodic qlucose input. Ber. Bunsenges. Phys. Chem. 89 (651–654) 1985

    Google Scholar 

  • Leibovic K. H. & Andrietii. F.: Analysis of a model transmitter kinetics. Biol.Cybernetics 27(165–173)1977

    Article  MATH  Google Scholar 

  • Richter, P.: Entrainment of chemical oscillators and resonance dissipation. Physica 10D (353–368)1984

    MathSciNet  Google Scholar 

  • Rössler, O. E.: The chaotic hierarchy. Z. Naturforsch. 38a (788–801)1982

    Google Scholar 

  • Rössler, O. E. & Hudson, J. L.: A piecewise-linear hierarchy (Int. Symp. on Hath, Biol. Nov.1985, Kyoto, Japan; Abstract )

    Google Scholar 

  • Tomita, K.: Chaotic response of nonlinear oscillators. Phys. Rep. 86 (113–167) 1982

    Article  MathSciNet  Google Scholar 

  • Tomita,.K. & Kai, T.: Chaotic response of a limit cycle. J. Stat. Phys. 21 (65–86) 1979

    Article  MathSciNet  Google Scholar 

  • Tóth, J.: A mass action kinetic model of neurochemical transmission. In: Dynamic phenomena in neurochemistry and neurophysics: Theoretical aspects (Erdi, P. ed. ), Budapest, 1985. pp. 522–55.

    Google Scholar 

  • Tucek, S.: Acetylcoenzyme A and the synthesis of acetylcholine in neurons. Review of recent progress. Gen. Physiol. Biophys. 2 (313–324) 1983

    Google Scholar 

  • Venkov, L. & Markov, S. M.: Dynamical model of cholinergic synapse transmission. Cell. Mol. Biol. 26 (541–546) 1980

    Google Scholar 

  • Winfree, A. T.: The geometry of biological time ( Springer, New York ) 1980

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1986 D. Reidel Publishing Company

About this chapter

Cite this chapter

Erdi, P., Barna, G. (1986). Pattern Formation in Neural Systems I. Autorhytmicity, entrainment, quasiperiodicity and chaos in neurochemical systems. In: Trappl, R. (eds) Cybernetics and Systems ’86. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-4634-7_43

Download citation

  • DOI: https://doi.org/10.1007/978-94-009-4634-7_43

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-8560-1

  • Online ISBN: 978-94-009-4634-7

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics