Ueda Lecture(Jan 16, 2009)

  • Date
    • Friday, Jan 16, 2009, 10:30-12:00
  • Place
    • 2F Seminar room 224, Main Research Builiding, RIKEN Wako Campus
  • Speaker
    • Yoshisuke Ueda (Waseda University / RIKEN)
  • Title
    • "Chaos: a phenomenology of broken-egg (1)"
  • Language
    • Japanese
  • Abstract

    The goal of this lecture is to provide fundamental knowledge of important subjects of chaotic phenomena in real physical systems. The physical systems introduced in this lecture series are simple two electrical and electronic circuits. Both circuits are represented by two dependent state variables and sine wave external forcing signal. These are regarded as the simplest and representative ones in the extensive field of natural science.

    The one of the circuits is a series resonance circuit which consists of
    single resistor, capacitor, and inductor. Inductor shows nonlinear
    saturation characteristics between with magnetic flux in the iron core and exciting current, i.e., saturable iron core. This oscillatory system shows a stationary equiliblium without external applied voltage, therefore (, it is) called Forced Oscillatory System.

    The other circuit is a so-called negative resistance oscillator, which
    keeps self sustained oscillation, i.e., producing oscillation with constant
    amplitude and frequency. Synchronization phenomana occur when a periodic forcing signal is applied to the system depending on the frequency and amplitude of the external periodic signals. In the case when synchronization does not attained, or goes "wrong," aperiodic beat oscillation emerges. therefore the system is called Forced Self-Oscillatory System.

    It is well known that chaos could be observed in both of the above systems.

    At present, it is said that the data collecting by using Ueda's analog
    computer on the 27th of November, 1961, is the oldest example of chaos
    discovered in an actual physical system. The data was nothing like the
    smooth oval closed curves (almost periodic oscillations), but was more like a "broken egg" with jagged edges.

    This lecture will unravel a complex phenomenon, so-called "chaos", based on lecturer's own experiences, while nowadays, concepts of chaos has been well-established by many physicists and mathematicians.

    We use "Theory of Chaotic Phenomena, CORONA Publishing, 2008 (in Japanese), as a textbook for this lecture series. It is written based on the lecture notes of the class at Under Graduate and Graduate School of Electrical and Electronic Engineering Department, Kyoto University since 1966, together with Complex Systems Department, Future University-Hakodate since 2000. It also contains part of research results that the lecturer carried out himself since 1959.