Skip to main content
Top

2017 | OriginalPaper | Chapter

Towards a Universal Modeller of Chaotic Systems

Author : Erik Berglund

Published in: Learning and Intelligent Optimization

Publisher: Springer International Publishing

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

Abstract

This paper proposes a Machine Learning (ML) algorithm and examines its dynamic properties when trained on chaotic time series. It will be demonstrated that the output of the ML system is itself more chaotic if it is trained on a chaotic input than if it is trained on non-chaotic input. The proposed ML system builds on to the Parameter-Less Self-Organising Map 2 (PLSOM2) and introduces new developments.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

Literature
1.
go back to reference Berglund, E.: Improved PLSOM algorithm. Appl. Intell. 32(1), 122–130 (2010)CrossRef Berglund, E.: Improved PLSOM algorithm. Appl. Intell. 32(1), 122–130 (2010)CrossRef
2.
go back to reference Berglund, E., Sitte, J.: The parameterless self-organizing map algorithm. IEEE Trans. Neural Netw. 17(2), 305–316 (2006)CrossRef Berglund, E., Sitte, J.: The parameterless self-organizing map algorithm. IEEE Trans. Neural Netw. 17(2), 305–316 (2006)CrossRef
3.
go back to reference Chappell, G.J., Taylor, J.G.: The temporal kohonen map. Neural Netw. 6(3), 441–445 (1993)CrossRef Chappell, G.J., Taylor, J.G.: The temporal kohonen map. Neural Netw. 6(3), 441–445 (1993)CrossRef
4.
go back to reference Chen, L., Aihara, K.: Chaotic simulated annealing by a neural-network model with transient chaos. Neural Netw. 8(6), 915–930 (1995)CrossRef Chen, L., Aihara, K.: Chaotic simulated annealing by a neural-network model with transient chaos. Neural Netw. 8(6), 915–930 (1995)CrossRef
5.
go back to reference Crook, N., Scheper, T.O.:. A novel chaotic neural network architecture. In: ESANN 2001 Proceedings, pp. 295–300, April 2001 Crook, N., Scheper, T.O.:. A novel chaotic neural network architecture. In: ESANN 2001 Proceedings, pp. 295–300, April 2001
6.
go back to reference Freeman, W.J.: Chaos in the brain: possible roles in biological intelligence. Int. J. Intell. Syst. 10(1), 71–88 (1995)CrossRefMATH Freeman, W.J.: Chaos in the brain: possible roles in biological intelligence. Int. J. Intell. Syst. 10(1), 71–88 (1995)CrossRefMATH
7.
go back to reference Freeman, W.J., Barrie, J.M.: Chaotic oscillations and the genesis of meaning in cerebral cortex. In: Buzsáki, G., Llinás, R., Singer, W., Berthoz, A., Christen, Y. (eds.) Temporal Coding in the Brain. NEUROSCIENCE. Springer, Heidelberg (1994). doi:10.1007/978-3-642-85148-3_2 Freeman, W.J., Barrie, J.M.: Chaotic oscillations and the genesis of meaning in cerebral cortex. In: Buzsáki, G., Llinás, R., Singer, W., Berthoz, A., Christen, Y. (eds.) Temporal Coding in the Brain. NEUROSCIENCE. Springer, Heidelberg (1994). doi:10.​1007/​978-3-642-85148-3_​2
8.
go back to reference Koskela, T., Varsta, M., Heikkonen, J., Kaski, K.:. Recurrent SOM with local linear models in time series prediction. In: 6th European Symposium on Artificial Neural Networks, pp. 167–172. D-facto Publications (1998) Koskela, T., Varsta, M., Heikkonen, J., Kaski, K.:. Recurrent SOM with local linear models in time series prediction. In: 6th European Symposium on Artificial Neural Networks, pp. 167–172. D-facto Publications (1998)
9.
go back to reference Mackey, M.C., Glass, L.: Oscillation and chaos in physiological control systems. Science 197, 287 (1977)CrossRef Mackey, M.C., Glass, L.: Oscillation and chaos in physiological control systems. Science 197, 287 (1977)CrossRef
10.
go back to reference Sprott, J.C.: Chaos and Time-Series Analysis. Oxford University Press, Oxford (2003)MATH Sprott, J.C.: Chaos and Time-Series Analysis. Oxford University Press, Oxford (2003)MATH
11.
go back to reference Varstal, M., Millán, J.R., Heikkonen, J.: A recurrent self-organizing map for temporal sequence processing. In: Gerstner, W., Germond, A., Hasler, M., Nicoud, J.-D. (eds.) ICANN 1997. LNCS, vol. 1327, pp. 421–426. Springer, Heidelberg (1997). doi:10.1007/BFb0020191 Varstal, M., Millán, J.R., Heikkonen, J.: A recurrent self-organizing map for temporal sequence processing. In: Gerstner, W., Germond, A., Hasler, M., Nicoud, J.-D. (eds.) ICANN 1997. LNCS, vol. 1327, pp. 421–426. Springer, Heidelberg (1997). doi:10.​1007/​BFb0020191
12.
go back to reference Voegtlin, T.: Recursive self-organizing maps. Neural Netw. 15(8–9), 979–991 (2002)CrossRef Voegtlin, T.: Recursive self-organizing maps. Neural Netw. 15(8–9), 979–991 (2002)CrossRef
13.
go back to reference Wang, L., Li, S., Tian, F., Fu, X.: A noisy chaotic neural network for solving combinatorial optimization problems: stochastic chaotic simulated annealing. IEEE Trans. Syst. Man Cybern. Part B 34(5), 2119–2125 (2004)CrossRef Wang, L., Li, S., Tian, F., Fu, X.: A noisy chaotic neural network for solving combinatorial optimization problems: stochastic chaotic simulated annealing. IEEE Trans. Syst. Man Cybern. Part B 34(5), 2119–2125 (2004)CrossRef
Metadata
Title
Towards a Universal Modeller of Chaotic Systems
Author
Erik Berglund
Copyright Year
2017
DOI
https://doi.org/10.1007/978-3-319-69404-7_23

Premium Partner