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From Bifurcations to Chua's Periodic Table

Published online by Cambridge University Press:  01 February 2011

Roberto Tonelli
Affiliation:
University of Caifornia-Berkely Istituto Nazionale per la Fisica della Materia (INFM) and Dipart. di Scienze Fisiche, Universitá di Cagliari, 09042 Monserrato (CA), Italy.
Len O. Chua
Affiliation:
University of Caifornia-Berkely
Franco Meloni
Affiliation:
Istituto Nazionale per la Fisica della Materia (INFM) and Dipart. di Scienze Fisiche, Universitá di Cagliari, 09042 Monserrato (CA), Italy.
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Abstract

We describe and discuss the similarites in two different kinds of physical systems: Chua's circuit (and, broady speaking, chaotic systems) and atoms in the Periodic Table. We anayze the regularities arising from the chaotic nature of the former against the regularities in the energy spectra of the second. We show the existing analogies among the Bohr's law and the bifurcation diagram building a map connecting each energy level in atoms to each point in the bifurcation diagram in the parameter space. We found a genera rule valid for many element of the Periodic Table by calculating the two-dimensional bifurcation diagram versus Bohr's law. The result is a one-to-one correspondence between atoms and nonlinear Chua's circuits. Finaly we discuss possible implications of the model when applied to more complicated systems like molecules or atomic clusters.

Type
Research Article
Copyright
Copyright © Materials Research Society 2002

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References

1. Devaney, L. R.An Introduction to Chaotic Dynamical Systems”, Benjamin/Cumming Publishing (1986)Google Scholar
2. Madan, R. N. in Chua's Circuit, a Paradigm for Chaos. Edited by Madan, Rabinder N.. (World Scientific Series on Nonlinear Sciences, Singapore, 1993).CrossRefGoogle Scholar
3. Romano, D., Bovati, M. and Meloni, F., Chua's Atom, Int. J. of Bifurcation and Chaos, Vol. 9. No. 6 (1999) 11531157.CrossRefGoogle Scholar
4. Series, G. W. in The spectrum of Atomic Hydrogen, (Oxford Univ. Press, 1957)Google Scholar
5. Cruz, J. M. and Chua, L.O.A CMOS IC Nonlinear Resistor for Chua's Circuit“, IEEE Trans. Circuits Syst. 39 (1992) 895995.CrossRefGoogle Scholar

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From Bifurcations to Chua's Periodic Table
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