Nonlinear Sciences – Adaptation and Self-Organizing Systems
Scientific paper
2000-07-17
Physica A 294 (2001) 273-282
Nonlinear Sciences
Adaptation and Self-Organizing Systems
12 pages,7 figures,Revesion of TW060600 submitted to Physica A
Scientific paper
10.1016/S0378-4371(01)00115-7
Under the formalism of annealed averaging of the partition function, a type of random multifractal measures with their multipliers satisfying exponentially distributed is investigated in detail. Branching emerges in the curve of generalized dimensions, and negative values of generalized dimensions arise. Three equivalent methods of classification of the random multifractal measures are proposed, which is based on: (i) the discrepancy between the curves of generalized dimensions, (ii) the solution properties of equation T(qcrit) =0, and (iii) the relative position of the curve f(alpha) and the diagonal f(alpha)=alpha in the first quadrant. These three classes correspond to \mu([0,1])=infinity, \mu([0,1])=1 and \mu([0,1])=0, respectively. Phase diagram is introduced to illustrate the diverse performance of the random measures that is multiplicatively generated.
Yu Zun-Hong
Zhou Wei-Xing
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