Feigenbaum

R. K. Lindsay, B. G. Buchanan, E.A. Feigenbaum, J. Lederberg, Applications of Artificial Intelligence for Organic Chemistry, McGraw-Hill, New York, 1980. 

Rt is ironic that such an intensely computational mathematical science as chaos theory owes much of its modern origin to calculations that were performed not on a large mainframe computer but rather a simple programmable pocket calculator, a Hewlett-Packard HP-65 Feigenbaum would explain years later that had the series of intermediate calculations not been carried out sufficiently slowly, it is likely that most of the key observations would have been missed [feigSOa]. 

Critical Parameter Convergence Feigenbaum s found that the convergence rate of the critical parameters, is in fact geometric, i.e., the scale as =... 

This route should already be familiar to us from our discussion of the logistic map in chapter 4, Prom that chapter, we recall that the Feigenbaum route calls for a sequence of period-doubling bifurcations pitchfork bifurcations versus the Hopf bifurcations of the Landau-Hopf route) such that if subharmonic bifurcations are observed at Reynolds numbers TZi and 7 2, another can be expected at TZ determined by... 

Note that while a system s static complexity certainly influences its dynamical complexity, the two measures are clearly not equivalent. A system may be structurally rather simple (i.e. have a low static complexity), but have a complex dynamical behavior. (Think of the chaotic behavior of Feigenbaum s logistic equation, for example). 

Indeed, in those rare cases where a nonlinear system can be solved exactly -consider, for example, Feigenbaum s logistic equation when A = 4 = 4x (l —... 

Howard SG, Feigenbaum JJ Effect of gamma-hydroxybutyrate on central dopamine release in vivo a microdialysis study in awake and anesthetized animals. Biochem Pharmacol 33 103-110, 1997... 

B.G. Buchanan and E.A. Feigenbaum, Dendral and Meta-Dendral their application dimension. Artif. Intell., 11 (1978) 5-24. 

B. van Lierop, L. Castle, A. Feigenbaum and A. Boenke, Spectra for the Identification of Additives in Food Packaging, Kluwer Academic Publishers, Dordrecht (1998). 

J. Ehret-Henry, J. Bouquant, D. Scholler, R. Klink and A.E. Feigenbaum, Food Addit. Contam. 9, 303-14... 

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