Fractal Stationary Density in Coupled Maps

Jürgen Jost and Kiran M. Kolwankar

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Submission date: 20. Dec. 2004
Pages: 10
published in: Fractals in engineering : new trends in theory and applications / J. Lévy-Véhel ... (eds.)
London : Springer, 2005. - P. 57 - 64 
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Abstract:
We study the invariant measure or the stationary density of a coupled discrete dynamical system as a function of the coupling parameter (). The dynamical system considered is chaotic and unsynchronized for this range of parameter values. We find that the stationary density, restricted on the synchronization manifold, is a fractal function. We estimate the fractal dimension of the graph of this function and show that it changes continuously with the coupling parameter.