Skip to main content
SpringerLink
Log in

Theory of Non-Linear Excitations

  • Chapter
Biological Coherence and Response to External Stimuli

Abstract

The description of order and function in biological systems has been a challenge to scientists for many years. From the point of view of theoretical physics, biological function must be treated in terms of dynamic properties. A consideration of the motion of individual particles (atoms, molecules, …) is meaningless because of the enormous number of possible states. In addition, the problem of the interaction between electromagnetic fields and biological systems has gained increasing interest both through theoretical considerations and through rather exciting experimental results (Fröhlich 1980, 1986a; Kaiser 1981,1983a,b, 1984; Grundler, this Vol.).

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 109.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 139.99
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

  • Aihara K, Matsumoto G, Ichikawa M (1985) An alternating periodic-chaotic sequence observed in neuronal oscillators. Phys Lett 111A: 251–255

    Article  Google Scholar 

  • Andronov AA, Vitt AA, Khaikin SE (1970) Theory of oscillators. Pergamon, Oxford

    Google Scholar 

  • Babloyanz A, Salazar JM, Nicolis C (1985) Evidence of chaotic dynamics of brain activity during the sleep cycle. Phys Lett 111A: 152–156

    Article  Google Scholar 

  • Beckert S, Schock U, Schulz CD, Weidlich T, Kaiser F (1985) Experiments of the bifurcation behaviour of a forced nonlinear pendulum. Phys Lett 107A: 347–350

    Article  MathSciNet  Google Scholar 

  • Bergé P, Pomeau Y, Vidal C (1984) L’ordre dans le chaos. Hermann, Paris

    Google Scholar 

  • Birkhoff GD (1932) Sur quelques courbes fermées remarquables. Bull Soc Math Fr 60: 1–26

    MathSciNet  Google Scholar 

  • Collet P, Eckmann JP (1980) Iterated maps on the interval as dynamical systems. Birkhäuser, Boston

    Google Scholar 

  • Cvitanovic P (ed) (1984) Universality in chaos. Adam Hilger, Bristol

    MATH  Google Scholar 

  • Fischer P, Smith WR (eds) (1985) Chaos, fractals and dynamics. Marcel Dekker, New York

    MATH  Google Scholar 

  • Fröhlich H (1968a) Long range coherence and energy storage in biological systems. Int J Quantum Chem 2: 641–649

    Article  ADS  Google Scholar 

  • Fröhlich H (1968b) Bosé condensation of strongly excited longitudinal electric modes. Phys Lett A26: 402–403

    Article  Google Scholar 

  • Fröhlich H (1969) Quantum mechanical concepts in biology. In: Marois M (ed) Theoretical physics and biological. North-Holland, Amsterdam, pp 13–22

    Google Scholar 

  • Fröhlich H (1977) Possibilities of long- and short-range electric interactions of biological systems. Neurosci Res Program Bull 15: 67–70

    Google Scholar 

  • Fröhlich H (1980) The biological effects of microwaves and related questions. Adv Electronics Electron Phys 53: 85–152

    Article  Google Scholar 

  • Fröhlich H (1986) Coherent excitations in active biological systems. In: Gutman F, Keyzer H (eds) Modern bioelectrochemistry. Plenum, New York, pp 241–261

    Chapter  Google Scholar 

  • Fröhlich H, Kremer F (1983) Coherent excitations in biological systems. Springer, Berlin Heidelberg New York

    Book  Google Scholar 

  • Grundler W, Keilmann F (1983) Sharp resonances in yeast prove nonthermal sensitivity to microwaves. Phys Rev Lett 51. 1214–1216

    Article  ADS  Google Scholar 

  • Guckenheimer J, Holmes P (1983) Nonlinear oscillations, dynamical systems, and bifurcations of vector fields. Springer, Berlin Heidelberg New York

    Google Scholar 

  • Gurel O, Rössler OE (eds) (1979) Bifurcation theory and applications in scientific disciplines. New York Academy of Sciences, New York

    MATH  Google Scholar 

  • Hao B-L (1984) Chaos. World Scientific, Singapore

    MATH  Google Scholar 

  • Hayashi C (1964) Nonlinear oscillations in physical systems. McCraw-Hill, New York

    MATH  Google Scholar 

  • Hayashi H, Yshizuka S, Ohta M, Hirakawa K (1982) Chaotic behaviour in the onchidium giant neurone under sinusoidal stimulation. Phys Lett 88A: 435–438

    Article  MathSciNet  Google Scholar 

  • Hirsch MW (1976) Differential topology. Springer, Berlin Heidelberg New York Holden AV (ed) ( 1986 ) Chaos. Manchester University Press

    Google Scholar 

  • Holden AV, Winlow W, Haydon PG (1982) The induction of periodic and chaotic activity in a molluscan neurone. Biol Cybern 43: 169–173

    Article  MathSciNet  Google Scholar 

  • Kaiser F (1977a) Limit cycle model for brain waves. Phys Lett 62A: 63–64

    Article  Google Scholar 

  • Kaiser F (1977b) Limit cycle model for brain waves. Biol Cybern 27: 155–163

    Article  MathSciNet  MATH  Google Scholar 

  • Kaiser F (1978a) Coherent oscillations in biological system I. Z Naturforsch 33a: 294–304

    ADS  Google Scholar 

  • Kaiser F (1978b) Coherent oscillations in biological systems II. Z Naturforsch 33a: 418–431

    ADS  Google Scholar 

  • Kaiser F (1980) Nonlinear oscillations in physical and biological systems. In: Uslenghi PLE (ed) Nonlinear electromagnetics. Academic Press, New York, pp 343–389, Mir, Moskau, pp 250– 281 (in Russian)

    Google Scholar 

  • Kaiser F (1981) Coherent modes in biological systems. In: Illinger KH (ed) Biological effects of nonionizing radiation. ACS Symp Ser 151: 219–241

    Chapter  Google Scholar 

  • Kaiser F (1983a) Theory of resonant effects of rf and mw energy. In: Grandolfo M, Michaelson SM, Rindi A (eds) Biological effects and dosimetry of nonionizing radiation. Plenum, New York, pp 251–282

    Google Scholar 

  • Kaiser F (1983b) Specific effects in externally driven self-sustained oscillating biophysical model systems. In: Fröhlich H, Kremer F (eds) Coherent excitations in biological systems. Springer, Berlin Heidelberg New York, pp 128–133

    Chapter  Google Scholar 

  • Kaiser F (1984) Entrainment, quasiperiodicity, chaos, collapse: bifurcation routes of externally driven self-sustained oscillating systems. In: Adey WR, Lawrence AF (eds) Nonlinear electrodynamics in biological systems. Plenum, New York, pp 393–412

    Chapter  Google Scholar 

  • Kaiser F (1985a) Coherence, synchronization, chaos: cooperative processes in excited biological systems. In: Chiabrera A, Nicolini C, Schwan HP (eds) Interactions between electromagnetic fields and cells. Plenum, New York, pp 131–155

    Google Scholar 

  • Kaiser F (1985b) Cooperative behaviour in brain activity: response to external drives. In: Mishra RK (ed) World Scientific, Singapore, pp 467–491

    Google Scholar 

  • Kaiser F (1987) The role of chaos in biological systems. In: Barett W, Pohl H (eds) Energy transfer dynamics. Springer, Berlin Heidelberg New York, pp 224–236

    Chapter  Google Scholar 

  • Layne SP, Mayer-Kress G, Holzfuss J (1986) Problems associated with dimensional analysis of EEG data. In: Mayer-Kress G (ed) Dimensions and entropies in chaotic systems. Springer, Berlin Heidelberg New York, pp 246–256

    Chapter  Google Scholar 

  • Lorenz EN (1983) Deterministic nonperiodic flow. J Atoms Sci 20: 130–141

    Article  MathSciNet  ADS  Google Scholar 

  • Mandell AJ, Russo PV, Knapp S (1982) In: Haken H (ed) Evolution of order and chaos in physics, chemistry and biology. Springer, Berlin Heidelberg New York, pp 270–282

    Google Scholar 

  • Marsden JE, McCracken M (1976) The Hopf bifurcation and its application. Springer, Berlin Heidelberg New York

    Book  Google Scholar 

  • May RM (1976) Simple mathematical models with very complicated dynamics. Nature 261:459– 467

    Google Scholar 

  • Nayfeh AH, Mook DT (1979) Nonlinear oscillations. Wiley, New York

    MATH  Google Scholar 

  • Ott E (1981) Strange attractors and chaotic motions of dynamical systems. Rev Mod Phys 53: 655–671

    Article  MathSciNet  ADS  MATH  Google Scholar 

  • Poincaré H (1892) Les méthodes nouvelles de la mécanique céleste. Gauthier-Villars, Paris

    Google Scholar 

  • Rapp PE (1986) Oscillations and chaos in cellular metabolism and physiological systems. In: Holden AV (ed) Chaos. Manchester University Press

    Google Scholar 

  • Rapp PE, Albano AM, Zimmerman ID, Deguzman GC, Greenbaum NN (1985) Dynamics of spontaneous neural activity in the simian motor cortex, the dimension of chaotic neurons. Phys Lett 110A: 335–338

    Article  Google Scholar 

  • Schuster HG (1984) Deterministic chaos. Physik Verlag, Weinheim

    MATH  Google Scholar 

  • Thomson JMT, Stewart HB (1986) Nonlinear dynamics and chaos. J Wiley, New York

    Google Scholar 

  • Wiesenfeld K, McNamara B (1986) Small-signal amplification in bifurcating dynamical systems. Phys Rev A33. 629–642

    Article  MathSciNet  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institut für Angewandte Physik - Theorie -, Technische Hochschule Darmstadt, Hochschulstraße 2, 6100, Darmstadt 1, Germany

    F. Kaiser

Authors
  1. F. Kaiser
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Department of Physics, Oliver Lodge Laboratory, Oxford Street, L69 3BX, Liverpool, England

    Herbert Fröhlich

Rights and permissions

Reprints and permissions

Copyright information

© 1988 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Kaiser, F. (1988). Theory of Non-Linear Excitations. In: Fröhlich, H. (eds) Biological Coherence and Response to External Stimuli. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-73309-3_2

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-73309-3_2

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-73311-6

  • Online ISBN: 978-3-642-73309-3

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation