Conservation laws in coupled multiplicative random arrays lead to 1/f noise
Abstract
We consider the dynamic evolution of a coupled array of N multiplicative random variables. The magnitude of each is constrained by a lower bound w0 and their sum is conserved. Analytical calculation shows that the simplest case, N=2 and w0=0, exhibits a Lorentzian spectrum which gradually becomes fractal as w0 increases. Simulation results for larger N reveal fractal spectra for moderate to high values of w0 and power-law amplitude fluctuations at all values. The results are applied to estimating the fractal exponents for cochlear-nerve-fiber action-potential sequences with remarkable success, using only two parameters.
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