 1  Author
 Takashi Tsuchiya  Requires cookie*   Title
 The Critical Amplitude for Bifurcation Points of the Logistic Map    Abstract
 The phenomenon called critical slowing down is studied for some analytically tractable bifurcation points of the logistic map. The critical amplitude and the critical amplitude ratio are introduced to describe the critical behaviors more precisely when the critical exponents are identically unity for two critical behaviors which are to be compared. Since Hao predicted unity of the critical exponent for 1d maps assuming exponential damping of the distance from the attractor, the assumption is checked. The result is that the shrinkage of the valid region of the assumption occurs as the adjustable parameter approaches one of the bifurcation points.   
Reference
 Z. Naturforsch. 51a, 1170—1174 (1996); received September 25 1996   
Published
 1996   
Keywords
 Bifurcation, Logistic map, Critical slowing down, Critical exponent, Critical amplitude   
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