The Order of Appearance of Oscillation Modes of a Piecewise Linear Map

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概要

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• We have studied the order of appearance of oscillation modes associated with a piecewiselinear map (PLM) obtained frotn the Oregonator model excited by an external periodic force(Acos(cur)). It is shown that the bifurcation of the transition from m-peak oscillation (m-PC)to (m -; 1)-PC occturs when the value of a shift parameter in the PLIVI varies from large to small.The region of appearance of the oscillation mode m,.(m, m-4-1) consisting of r times of m-PC ands times of (m -: l)-PC is obtained from analytical treatraaent, where r, s and m are the positiveintegers, respectively. The series of the winding ntmmber of the oscillation mode 'tv.,.(m,m -4- l)form a part of strccessive Farey series, and the Farey series can be decomposed into the part ofseries of unstable oscillation rnode and that of stable oscillation mode. The bifurcation diagramof the order of appearance of the oscillation mode rc.,.(m, m f l) in the PLIVI has a self similarhierarchy. Analyzing theoretically the order of appearance of the oscillation mode 7T.,. (m, m -4- 1)and m-PG in the PLM, we can explain the order of appearance of the oscillation modes in theparameter space (A,ca) for the Oregonator excited by ,4cos(c;r).

• 社団法人日本物理学会の論文
• 1996-11-15

著者

• YAMAGUCHI Takahiro

  Faculty of Science,Okayama University of Science

• Ohtagaki Hirokazu

  Faculty Of Engineering Okayama University Of Science

• Yamaguchi Takahiro

  Faculty Of Science Okayama University Of Science

• Yamaguchi Takahiro

  Faculty Of Agriculture Graduate School Tohoku University

関連論文

• The Appearence Order and Structure of Oscillation Mode of OREGONATOR Exerted by an External Periodic Oscillation Force
• The Structure and Order of Appearance of Oscillation Modes of the Oregonator to an External Periodic Force Acting on the Second Component
• The Structure and Order of Appearance of Oscillation Mode of Oregonator Exerted by an External Periodic Force
• Hysteresis and Relaxation Phenomena near a Bifurcation Point of the Oscillation Mode of the Forced Oregonator
• Bifurcation of Oscillation Modes Obtained by a Shift Type Mapping Simulating the Oregonator Responding to an External Periodic Force
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• Release Characteristics of Endogenous Constituents by Exposure of Small Intestine to Modified β-Cyclodextrins
• Oscillation Modes of Forced Nonlinear Systems of van der Pol Type (General)
• The Order of Appearance of Oscillation Modes of a Piecewise Linear Map

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