Bifurcation Set of a Modelled Parallel Blower System

Hideaki OKAZAKI  Tomoyuki UWABA  Hideo NAKANO  Takehiko KAWASE  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E76-A   No.3   pp.299-309
Publication Date: 1993/03/25
Online ISSN: 
Print ISSN: 0916-8508
Type of Manuscript: Special Section PAPER (Special Section on the 5th Karuizawa Workshop on Circuits and Systems)
parallel blower system,  saddle node bifurcation,  period doubling bifurcation,  stable and unstable manifolds,  homoclinic bifurcation,  

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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.