Skip to main content
SpringerLink
Log in

From Self-Organizing Systems to Pattern Formation Systems

  • Chapter
  • First Online:
Determinism and Self-Organization of Human Perception and Performance

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

  • 489 Accesses

Abstract

In this chapter and the following chapter fundamental concepts of the theory of pattern formation and synergetics will be introduced. The goal of this chapter is to clarify the notion of self-organizing systems and pattern formation systems. It will be shown that while it is difficult to arrive at a clear definition of self-organizing systems, pattern formation systems can be defined in a precise way. With the definition of pattern formation systems at hand, this chapter provides a basis for understanding humans and animals from a pattern formation perspective.

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 149.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 199.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 199.99
Price excludes VAT (USA)
  • Durable hardcover 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

References

  1. C. Allain, H.C. Cummins, P. Lallemand, Critical slowing down near the Rayleigh-Benard convection instability. Le J. de Phys. Lett. 24, L474–L477 (1978)

    Google Scholar 

  2. A. Bakonyi, D. Michaelis, U. Peschel, G. Onishchukov, F. Lederer, Dissipative solitons and their critical slowing down near a supercritical bifurcation. J. Opt. Soc. Am. B 19, 487–491 (2002)

    Article  ADS  Google Scholar 

  3. P.J. Beek, R.C. Schmidt, A.W. Morris, M.-Y. Sim, M.T. Turvey, Linear and nonlinear stiffness and friction in biological rhythmic movements. Biol. Cybern. 73, 499–507 (1995)

    Article  Google Scholar 

  4. J.J. Binnen, N.J. Dowrick, A.J. Fisher, M.E.J. Newman, The Theory of Critical Phenomena (Oxford University Press, New York, 1992)

    Google Scholar 

  5. H.U. Bödeker, T.D. Frank, R. Friedrich, H.G. Purwins, Stochastic dynamics of dissipative solitons in gas-discharge systems, in Anomalous Fluctuation Phenomena in Complex Systems: Plasmas, Fluids and Financial Markets ed. by C. Riccardi, H.E. Roman (Research Signpost, Trivandrum, 2008), pp. 145–184

    Google Scholar 

  6. D.G. Dotov, T.D. Frank, From the W-method to the canonical-dissipative method for studying uni-manual rhythmic behavior. Motor Control 15, 550–567 (2011)

    Article  Google Scholar 

  7. W. Ebeling, I.M. Sokolov, Statistical Thermodynamics and Stochastic Theory of Nonequilibrium Systems (World Scientific, Singapore, 2004)

    MATH  Google Scholar 

  8. R.E. Ecke, H. Haucke, Y. Maeno, J.C. Wheatley, Critical dynamics at a Hopf bifurcation to oscillatory Rayleigh-Benard convection. Phys. Rev. A 33, 1870–1878 (1986)

    Article  ADS  Google Scholar 

  9. T.D. Frank, Nonlinear Fokker-Planck Equations: Fundamentals and Applications (Springer, Berlin, 2005)

    MATH  Google Scholar 

  10. T.D. Frank, On a moment-based data analysis method for canonical-dissipative oscillator systems. Fluctuation Noise Lett. 9, 69–87 (2010)

    Article  Google Scholar 

  11. T.D. Frank, Pumping and entropy production in non-equilibrium drift-diffusion systems: a canonical-dissipative approach. Eur. J. Sci. Res. 46, 136–146 (2010)

    Google Scholar 

  12. T.D. Frank, Multistable pattern formation systems: candidates for physical intelligence. Ecol. Psychol. 24, 220–240 (2012)

    Article  Google Scholar 

  13. T.D. Frank, V.L.S. Profeta, H. Harrison, Interplay between order parameter and system parameter dynamics: considerations on perceptual-cognitive-behavioral mode-mode transitions exhibiting positive and negative hysteresis and response times. J. Biol. Phys. 41, 257–292 (2015)

    Article  Google Scholar 

  14. T.M. Griffin, R. Kram, S.J. Wickler, D.F. Hoyt, Biomechanical and energetic determinants of the walk-trot transition in horses. J. Exp. Biol. 207, 4215–4223 (2004)

    Article  Google Scholar 

  15. S.J. Guastello, Chaos, Catastrophe, and Human Affairs (Lawrence Erlbaum, Mahwah, 1995)

    Google Scholar 

  16. J. Guckenheimer, P. Holmes, Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields (Springer, Berlin, 1983)

    Book  Google Scholar 

  17. H. Haken, Distribution function for classical and quantum systems far from thermal equilibrium. Z. Phys. 263, 267–282 (1973)

    Article  ADS  MathSciNet  Google Scholar 

  18. H. Haken, Principles of Brain Functioning (Springer, Berlin, 1996)

    Book  Google Scholar 

  19. H. Haken, Synergetics: Introduction and Advanced Topics (Springer, Berlin, 2004)

    Book  Google Scholar 

  20. D.F. Hoyt, C.R. Taylor, Gait and energetics of locomotion in horses. Nature 292, 239–240 (1981)

    Article  ADS  Google Scholar 

  21. A. Jenkins, Self-oscillations. Phys. Rep. 525, 167–222 (2013)

    Article  ADS  MathSciNet  Google Scholar 

  22. B.A. Kay, J.A.S. Kelso, E.L. Saltzman, G. Schöner, The space-time behavior of single and bimanual movements: data and model. J. Exp. Psychol. - Hum. Percept. Perform. 13, 178–192 (1987)

    Article  Google Scholar 

  23. J.A.S. Kelso, Dynamic Patterns - The Self-Organization of Brain and Behavior (MIT Press, Cambridge, 1995)

    Google Scholar 

  24. M.D. Kuzmin, Shape of temperature dependence of spontaneous magnetization of ferromagnets: quantitative analysis. Phys. Rev. Lett. 94, article 107204 (2005)

    Google Scholar 

  25. J. Liu, G. Ahlers, Spiral-defect chaos in Rayleigh-Benard convection with small Prandtl numbers. Phys. Rev. Lett. 77, 3126–3129 (1996)

    Article  ADS  Google Scholar 

  26. S.M. Lopresti-Goodman, M.T. Turvey, T.D. Frank, Behavioral dynamics of the affordance “graspable”. Atten. Percept. Psychophys. 73, 1948–1965 (2011)

    Article  Google Scholar 

  27. S. Mongkolsakulvong, T.D. Frank, Synchronization and anchoring of two non-harmonic canonical-dissipative oscillators via Smorodinsky-Winternitz potentials. Condens. Matter Phys. 20, article 44001 (2017)

    Article  Google Scholar 

  28. L.K. Nguyen, M.A.S. Cavadas, B.N. Kholodenko, T.D. Frank, A. Cheong, Species differential regulation of cox2 can be described by nfkb-dependent logic and gate. Cell. Mol. Life Sci. 72, 2431–2443 (2014)

    Article  Google Scholar 

  29. G. Nicolis, Introduction to Nonlinear Sciences (Cambridge University Press, Cambridge, 1995)

    Book  Google Scholar 

  30. A. Nitzan, P. Ortoleva, J. Deutch, J. Ross, Fluctuations and transitions at chemical instabilities: the analogy to phase transition. J. Chem. Phys. 61, 1056–1074 (1974)

    Article  ADS  Google Scholar 

  31. J.W. Rayleigh, Theory of Sound (Dover, New York, 1945). First edition published 1894

    Google Scholar 

  32. P. Romanczuk, M. Bär, W. Ebeling, B. Lindner, L. Schimansky-Geier, Active Brownian particles: from individual to collective stochastic dynamics. Eur. Phys. J. Special Topics 202, 1–162 (2012)

    Article  ADS  Google Scholar 

  33. R.C. Schmidt, C. Carello, M.T. Turvey, Phase transitions and critical fluctuations in the visual coordination of rhythmic movements between people. J. Exp. Psychol. - Hum. Percept. Perform. 53, 247–257 (1990)

    Google Scholar 

  34. J.P. Scholz, J.A.S. Kelso, G.S. Schöner, Non-equilibrium phase transitions in coordinated biological motion: critical slowing down and switching time. Phys. Lett. A 123, 390–394 (1987)

    Article  ADS  Google Scholar 

  35. W. Sha, J. Moore, K. Chen, A.D. Lassaletta, C.S. Yi, J.J. Tyson, J.C. Silbe. Hysteresis drives cell-cycle transitions in Xenopus laevis egg extracts. Proc. Natl. Acad. Sci. USA 93, 628–633 (2003)

    Google Scholar 

  36. D. Sornette, Critical Phenomena in Natural Science (Springer, Berlin, 2000)

    Book  Google Scholar 

  37. H.E. Stanley, Introduction to Phase Transitions and Critical Phenomena (Oxford University Press, New York, 1971)

    Google Scholar 

  38. F. Verhulst, Nonlinear Differential Equations and Dynamical Systems, 2nd ed. (Springer, Berlin, 1996)

    Book  Google Scholar 

  39. G.V. Wallenstein, J.A.S. Kelso, S.L. Bressler, Phase transitions in spatiotemporal patterns of brain activity and behavior. Phys. D 84, 626–634 (1995)

    Article  Google Scholar 

  40. L. Wang, B.L. Walker, S. Iannaccone, D. Bhatt, P.J. Kennedy, W.T. Tse, Bistable switches control memory and plasticity in cellular differentiation. Proc. Natl. Acad. Sci. USA 106, 6638–6643 (2009)

    Article  ADS  Google Scholar 

  41. J. Wesfreid, Y. Pomeau, M. Dubois, C. Normand, P. Berge, Critical effects in Rayleig-Benard convection. Le J. de Phys. Lett. 7, 726–731 (1978)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Dept. Psychology and Physics, University of Connecticut, Storrs, CT, USA

    Till Frank

Authors
  1. Till Frank
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

Copyright information

© 2019 Springer Nature Switzerland AG

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Frank, T. (2019). From Self-Organizing Systems to Pattern Formation Systems. In: Determinism and Self-Organization of Human Perception and Performance. Springer Series in Synergetics. Springer, Cham. https://doi.org/10.1007/978-3-030-28821-1_3

Download citation

Publish with us

Policies and ethics

Search

Navigation