Bifurcation Phenomena of a Distributed Parameter System with a Nonlinear Element Having Negative Resistance

Hideo NAKANO  Hideaki OKAZAKI  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E75-A   No.3   pp.339-346
Publication Date: 1992/03/25
Online ISSN: 
Print ISSN: 0916-8508
Type of Manuscript: Special Section PAPER (Special Section on the 4th Karuizawa Workshop on Circuits and Systems)
distributed system,  nonlinear oscillation,  chaos,  bifurcation phenomena,  one-dimensional map,  

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Dynamic behavior of a distributed parameter system described by the one-dimensional wave equation with a nonlinear boundary condition is examined in detail using a graphical method proposed by Witt on a digital computer. The bifurcation diagram, homoclinic orbit and one-dimensional map are obtained and examined. Results using an analog simulator are introduced and compared with that of the graphical method. The discrepancy between these results is considered, and from the comparison among the bifurcation diagrams obtained by the graphical method, it is denoted that the energy dissipation in the system considerably restrains the chaotic state in the bifurcation process.