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[Keyword] period doubling(3hit)

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  • Bifurcation Set of a Modelled Parallel Blower System

    Hideaki OKAZAKI  Tomoyuki UWABA  Hideo NAKANO  Takehiko KAWASE  

     
    PAPER

      Vol:
    E76-A No:3
      Page(s):
    299-309

    Global dynamic behavior particularly the bifurcation of periodic orbits of a parallel blower system is studied using a piecewise linear model and the one-dimensional map defined by the Poincare map. First several analytical tools are presented to numerically study the bifurcation process particularly the bifurcation point of the fixed point of the Poincare map. Using two bifurcation diagrams and a bifurcation set, it is shown how periodic orbits bifurcate and leads to chaotic state. It is also shown that the homoclinic bifurcations occur in some parameter regions and that the Li & Yorke conditions of the chaotic state hold in the parameter region which is included in the one where the homoclinic bifurcation occurs. Together with the above, the stable and unstable manifolds of a saddle closed orbit is illustrated and the existence of the homoclinic points is shown.

  • Periodic Solutions in the Hodgkin-Huxley Equations for Muscle

    Kazuko TERADA  Shuji YOSHIZAWA  Chiaki NISHIMURA  

     
    LETTER

      Vol:
    E75-A No:7
      Page(s):
    928-930

    Bifurcations of the periodic solutions of the space-clamped Hodgkin-Huxley equations for the muscle membrane are studied regarding the chloride conductance as a parameter. A limit cycle appears at a Hopf bifurcation and disappears at a homoclinic orbit. With high sodium permeability, a subcritical period doubling bifurcation occurs before it disappears.

  • The Computation of Nodal Points Generated by Period Doubling Bifurcation Points on a Locus of Turning Points

    Norio YAMAMOTO  

     
    PAPER-Nonlinear Systems

      Vol:
    E75-A No:5
      Page(s):
    616-621

    As the values of parameters in periodic systems vary, a nodal point appearing on a locus of period doubling bifurcation points crosses over a locus of turning points. We consider the nodal point lying just on the locus of turning points and consider its accurate location. To compute it, we consider an extended system which consists of an original equation and an additional equation. We present a result assuring that this extended system has an isolated solution containing the nodal point.