DocumentCode :
1462705
Title :
Passivity and complexity
Author :
Chua, Leon O.
Author_Institution :
Dept. of Electr. Eng. & Comput. Sci., California Univ., Berkeley, CA, USA
Volume :
46
Issue :
1
fYear :
1999
fDate :
1/1/1999 12:00:00 AM
Firstpage :
71
Lastpage :
82
Abstract :
Nature abounds with complex patterns and structures emerging from homogeneous media operating far from thermodynamic equilibrium. Such phenomena, which are widely observed in both inanimate (nonbiological) and biological media, can be modeled and studied via the CNN (cellular neural/nonlinear network) paradigm in an in-depth and unified way. Whether a homogeneous medium is capable of exhibiting complexity depends on whether the CNN cells, or its couplings, are locally active in a precise circuit-theoretic sense. This local activity principle is of universal generality and is responsible for all symmetry breaking phenomena observed in a great variety of nonequilibrium media ranging from the nucleation of domain oscillations in bulk semiconductor materials (e.g., gallium arsenide in Gunn diodes) to the emergence of artificial life itself. The long forgotten yet classic P. R. (positive real) criteria is resurrected and given new prominence in this paper by invoking its “negative” version and deriving a set of analytical inequalities for calculating the parameter range necessary for the emergence of a nonhomogeneous static or dynamic pattern in a homogeneous medium operating under an influx of energy and/or matter. The resulting “complexity related” inequalities are applicable to all media, continuous or discrete, which have been mapped into a CNN paradigm
Keywords :
cellular neural nets; circuit complexity; network parameters; nonlinear network analysis; CNN; analytical inequalities; cellular neural network; complex patterns; complexity related inequalities; domain oscillations; homogeneous medium; local activity principle; parameter range; positive real criteria; symmetry breaking phenomena; Biological system modeling; Cellular networks; Cellular neural networks; Coupling circuits; Gallium arsenide; Gunn devices; Local activities; Semiconductor diodes; Semiconductor materials; Thermodynamics;
fLanguage :
English
Journal_Title :
Circuits and Systems I: Fundamental Theory and Applications, IEEE Transactions on
Publisher :
ieee
ISSN :
1057-7122
Type :
jour
DOI :
10.1109/81.739186
Filename :
739186
Link To Document :
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