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1997 (1)
1996 (1)
1Author    Takashi TsuchiyaRequires 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 bifurca-tion 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 1-d 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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 TEI-XML for    default:Reihe_A/51/ZNA-1996-51a-1170.pdf 
 Identifier    ZNA-1996-51a-1170 
 Volume    51 
2Author    Takashi Tsuchiya, Daisuke YamagishiRequires cookie*
 Title    The Complete Bifurcation Diagram for the Logistic Map  
 Abstract    The complete bifurcation diagram as well as the basin of attraction for the logistic map is presented for the whole range of the control parameters, namely —2<a<4 where the system remains finite. Equivalence of the newly found bifurcation branch to the conventional branch is shown. 
  Reference    Z. Naturforsch. 52a, 513—516 (1997); received February 11 1997 
  Published    1997 
  Keywords    Logistic map, bifurcation diagram, basin of attraction, equivalent transformation 
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 TEI-XML for    default:Reihe_A/52/ZNA-1997-52a-0513.pdf 
 Identifier    ZNA-1997-52a-0513 
 Volume    52