Skip to main content

Autowaves: Results, Problems, Outlooks

  • Conference paper

Part of the book series: Springer Series in Synergetics ((SSSYN,volume 28))

Abstract

The autowaves [1–3] form a type of waves which are characteristic of strongly nonlinear active media. To here belong self-sustained signals inducing local release of stored energy in an active medium, which is spent to trigger the same process in adjacent regions. The examples are provided by waves of combustion, of phase transitions, concentrational waves in chemical reactions, and also by many biological autowave processes (propagation of nerve impulses, excitation waves in heart muscle, epidemic waves in ecological communities, spreading waves in the cerebral cortex). These examples stress the importance of autowave phenomena.

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

Buying options

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

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Autowave Processes in Systems with Diffusion (ed. M.T. Grekhova), Gorky, Acad. Sei. USSR (1981)

    Google Scholar 

  2. G.R. Ivanitsky, V.I. Krinsky, A.N. Zaikin, A.M. Zhabotinsky, Sov. Sei. Rev. D2, 280 (198o)

    Google Scholar 

  3. G.R. Ivanitsky, V.I. Krinsky, E.E. Sel’kov. Mathematical Biophysics of the Cell, M., “Nauka” Publ. (1978) chapters 6–8

    Google Scholar 

  4. A.N. Kolmogorov, I.E. Petrovsky, N.S. Piskunov. Vestnik Moscovskogo Univ., Ser. 1, Mathematika, Mekhanika, 1, 1 (193 7)

    Google Scholar 

  5. Ya.B. Zeldovich, G.I. Barenblat, V.B. Librovich, G.M. Makhviladze. Mathematical Theory of Combustion and Explosion (in Russian), M., “Nauka” Publ. (1980)

    Google Scholar 

  6. A.M. Zhabotinsky, Biophizika, 9, 306 (1964)

    Google Scholar 

  7. V.I. Krinsky, Biofizika, 11, 676 (1966)

    Google Scholar 

  8. V.I. Krinsky. Problemy kibernetiki, 20, 59 (1968)

    Google Scholar 

  9. N. Wiener, A. Rosenblueth. Arch. Inst. Cardiologia de Mex., 16, 205 (1946)

    MathSciNet  Google Scholar 

  10. N.S. Balakhovsky, Biofizika, 10, 1063 (1965)

    Google Scholar 

  11. A.M. Zhabotinsky, A.N. Zaikin, in: Oscillatory Processes in Biological and Chemical Systems, 2, Pushchino, Acad. Sei. USSR, (1971) p. 279

    Google Scholar 

  12. A. J. Durston. Dev. Biol, 3J7, 221 (1974)

    Google Scholar 

  13. M. Allessie, F. Bonke, S. Shopman. Circ. Res. 33_, 54 (1973)

    Google Scholar 

  14. J. Bures, N.A. Goralova, J. Neurobiol, 14, 353 (1983)

    Article  Google Scholar 

  15. K.I. Agladze. Preprint, Pushchino (1983)

    Google Scholar 

  16. A.M. Pertsov, A.K.Grenadier, this volume

    Google Scholar 

  17. A.M. Pertsov, A.V. Panfilov,f in: Autowave Processes in Systems with Diffusion, Gorky, Acad. Sei. USSR, (1981) p. 77

    Google Scholar 

  18. V.I. Krinsky, in: Internat. Encycl. of Pharm, and Therapeutics, Pergamon Press, London, p. 105 (1981)

    Google Scholar 

  19. A.N. Zaikin, A.M. Zhabotinsky, Nature, 225, 535 (1970)

    Article  ADS  Google Scholar 

  20. A.T. Winfree, Science, 181, 937 (1973)

    Article  ADS  Google Scholar 

  21. D.C. Cohen, T.C. Neu, R.R. Rosales, Siam J. Appl. Math. 35, 536 (1978)

    MATH  Google Scholar 

  22. Koppel M., Howard L.N., Stud. Appl. Math. 52, 291 (1973); 56, 95 (1977)

    Google Scholar 

  23. Y. Kuramoto, T. Tsuzuki, Progr. Theor. Phys. 55, 356 (1976)

    Article  ADS  Google Scholar 

  24. T. Erneux, Herschkowitz-Kaufman. J. Chem. Phys. 66, 248 (1977)

    Article  ADS  Google Scholar 

  25. A.C. Mikhailov, I.V,Uporov. Doklady Akad. Nauk SSSR, 249, 733 (1979)

    Google Scholar 

  26. Ya.B. Zeldovich, B.A. Malomed. Doklady Akad. Nauk SSSR, 254, 93 (1980)

    MathSciNet  Google Scholar 

  27. V.I. Krindky, B.A. Malomed. Physica 9D, 81 (1983)

    MathSciNet  Google Scholar 

  28. A.T. Winfree, S.H. Strogatz. Physica 8D, 35 (1983)j 65 (1983); Physica 9D, 333 (1983)

    MathSciNet  Google Scholar 

  29. A.V. Panfilov, A.M. Pertsov. Doklady Acad. Nauk SSSR, N 6 (1984)

    Google Scholar 

  30. L.V. Yakushevitz. Studia Biophysica (1984) (in press)

    Google Scholar 

  31. A.S. Mikhailov, V.I. Krinsky. Physica 9D, 346 (1983)

    MathSciNet  Google Scholar 

  32. J.M. Greenberg. Siam J. Appl. Math. 30, 199 (1976)

    MATH  Google Scholar 

  33. K.I. Agladze, V.I. Krinsky. Nature 296, 424 (1982); 308, 834 (1984)

    Article  Google Scholar 

  34. V.I. Krinsky, K.I. Agladze. Physica 8D, 50 (1983)

    Google Scholar 

  35. A.M. Zanin, D.P. Kiryukhin, I.M. Barkalov, V.V. Barelko, V.I. Goldansky Doklady Akad. Nauk SSSR 260, N 6, 1397 (1981)

    Google Scholar 

  36. S.A. Zhukov, V.V. Barelko, L.F. Bokova in: Autowave Processes in Systems with Diffusion. Gorky, Acad. Sei. USSR, (1981), p. 149

    Google Scholar 

  37. V.V. Barelko. Problems of Cybernetics and Catalysis, 18 (1981)

    Google Scholar 

  38. A.M.Zhabotinsky. Concentrational Auto-Oscillations (in Russian) M. "Nauka" Pub1. (1974)

    Google Scholar 

  39. V. A. Vasiliev, Yu.M. Romanovsky, V.G.Yakhno, Uspekhifizitcheskikh nauk, L28, 625 (1979)

    Article  Google Scholar 

  40. A.T. Winfree, Geometry of Biological Time. Springer Verlag (1980)

    Google Scholar 

  41. V.I. Krinsky, A.S. Mikhailov. Autowaves. Znanie, Publ.Moskow (1984)

    MATH  Google Scholar 

  42. L.S. Polak, A.S. Mikhailov. Self-Organization in Nonequilibrium Physico-Chemical Systems (in Russian), M., “Nauka” Publ. (1983)

    Google Scholar 

  43. H. Haken, Synergetics, An Introduction. Nonequilibrium Phase Transitions and Self-Organization in Physics, Chemistry and Biology (3rd edition). Springer Verlag (1983)

    Google Scholar 

  44. H. Haken. Advanced Synergetics. Instability Hierarchies of Self- Organizing Systems and Devices. Springer Verlag (1983)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1984 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Krinsky, V.I. (1984). Autowaves: Results, Problems, Outlooks. In: Krinsky, V.I. (eds) Self-Organization Autowaves and Structures Far from Equilibrium. Springer Series in Synergetics, vol 28. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-70210-5_2

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-70210-5_2

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-70212-9

  • Online ISBN: 978-3-642-70210-5

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics