A simple model of diffusively coupled genetic networks on a 1d lattice is considered as a case study for characterizing complex unpredictable dynamics in Lyapunov-stable spatially extended systems. This dynamical regime, corresponding to transient evolution lasting over times that grow exponentially with the system size, is shown to be associated to the existence of a multifractal attractor in the thermodynamic limit. Space-time averages of proper observables exhibit robust statistical properties for finite, sufficiently large samples.
Complex Evolution in Genetic Networks / F. BIGNONE; R. LIVI; M. PROPATO. - In: EUROPHYSICS LETTERS. - ISSN 0295-5075. - STAMPA. - 40:(1997), pp. 497-502.
Complex Evolution in Genetic Networks
LIVI, ROBERTO;
1997
Abstract
A simple model of diffusively coupled genetic networks on a 1d lattice is considered as a case study for characterizing complex unpredictable dynamics in Lyapunov-stable spatially extended systems. This dynamical regime, corresponding to transient evolution lasting over times that grow exponentially with the system size, is shown to be associated to the existence of a multifractal attractor in the thermodynamic limit. Space-time averages of proper observables exhibit robust statistical properties for finite, sufficiently large samples.
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