New Bifurcation Phenomena in the Delayed Regulation Model, x(t+1)=AX(t){1-X(t-1)}

Yasuo MORIMOTO  

Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E75-A   No.2   pp.265-268
Publication Date: 1992/02/25
Online ISSN: 
DOI: 
Print ISSN: 0916-8508
Type of Manuscript: LETTER
Category: Nonlinear Phenomena and Analysis
Keyword: 
DR-model,  saw-tooth bifurcation,  new region,  

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Summary: 
In the delayed regulation medel, X(t+1)=AX(t){1-X(t-1)}, new bifurcation regions which have been overlooked in the past studies were found out for -1.01A0 and 2.27563A2.2838. In the former fixed point lying at 0 is destabilized at A=-1, and new type bifurcation is induced for A-1, where oscillation with saw-tooth waveform is observed. In the latter the stability once lost for A2.271 is restored for A2.27563, and the stable region continues up to A=2.2838.