Dynamics of Complex-Valued Neural Networks and Its Relation to a Phase Oscillator System

  • Ikuko Nishikawa
  • Yasuaki Kuroe
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3316)

Abstract

A network of complex-valued rotating neurons is proposed and its dynamics is compared with that of a coupled system of phase oscillators. The dynamics of the phases of neurons is shown to be described as a system of the phase oscillators with a pair-wise sinusoidal coupling. The amplitudes affect the phase dynamics in a way to modulate the coupling strength. As the system of phase oscillators is known to be effective for an area-wide signal control of an urban traffic network, the complex-valued neural network is also useful to the signal control. The similarity and the difference caused by the existence of the amplitude are discussed from the point of view of the flow control.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Hirose, A.: Complex-Valued Neural Networks. Series on Innovative Intelligence, vol. 5. World Scientific, Singapore (2003)MATHCrossRefGoogle Scholar
  2. 2.
    Kuroe, Y., et al.: On activation functions for complex-valued neural networks – existence of energy functions. In: Kaynak, O., Alpaydın, E., Oja, E., Xu, L. (eds.) ICANN 2003 and ICONIP 2003. LNCS, vol. 2714, pp. 985–992. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  3. 3.
    Kuramoto, Y.: Chemical Oscillations, Waves and Turbulence. Springer, Heidelberg (1984)MATHGoogle Scholar
  4. 4.
    Nishikawa, I., et al.: Area-wide Control of Traffic Signals by a Phase Model. Trans. Society of Instrument and Control Engineers 39(2), 199–208 (2003)Google Scholar
  5. 5.
    Nishikawa, I., Kita, H.: Information Flow Control by Autonomous Adaptive Nodes and Its Application to an On-line Traffic Control. In: Nishikawa, I. (ed.) Proceedings of the 6th JCIS (September 2003); Dynamics of Oscillator Network and Its Application to Offset Control of Traffic Signals. In. Proceeding of IJCNN 2004 (July 2004)Google Scholar
  6. 6.
    Goto, Thesis, Kyoto University (2000) (In Japanese)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Ikuko Nishikawa
    • 1
  • Yasuaki Kuroe
    • 2
  1. 1.College of Information Science and EngineeringRitsumeikan UniversityShigaJapan
  2. 2.Center for Information ScienceKyoto Institute of TechnologyKyotoJapan

Personalised recommendations