2,425 research outputs found
Synchronization of non-chaotic dynamical systems
A synchronization mechanism driven by annealed noise is studied for two
replicas of a coupled-map lattice which exhibits stable chaos (SC), i.e.
irregular behavior despite a negative Lyapunov spectrum. We show that the
observed synchronization transition, on changing the strength of the stochastic
coupling between replicas, belongs to the directed percolation universality
class. This result is consistent with the behavior of chaotic deterministic
cellular automata (DCA), supporting the equivalence Ansatz between SC models
and DCA. The coupling threshold above which the two system replicas synchronize
is strictly related to the propagation velocity of perturbations in the system.Comment: 16 pages + 12 figures, new and extended versio
Synchronization universality classes and stability of smooth, coupled map lattices
We study two problems related to spatially extended systems: the dynamical
stability and the universality classes of the replica synchronization
transition. We use a simple model of one dimensional coupled map lattices and
show that chaotic behavior implies that the synchronization transition belongs
to the multiplicative noise universality class, while stable chaos implies that
the synchronization transition belongs to the directed percolation universality
class.Comment: 6 pages, 7 figure
Non-invertible transformations and spatiotemporal randomness
We generalize the exact solution to the Bernoulli shift map. Under certain
conditions, the generalized functions can produce unpredictable dynamics. We
use the properties of the generalized functions to show that certain dynamical
systems can generate random dynamics. For instance, the chaotic Chua's circuit
coupled to a circuit with a non-invertible I-V characteristic can generate
unpredictable dynamics. In general, a nonperiodic time-series with truncated
exponential behavior can be converted into unpredictable dynamics using
non-invertible transformations. Using a new theoretical framework for chaos and
randomness, we investigate some classes of coupled map lattices. We show that,
in some cases, these systems can produce completely unpredictable dynamics. In
a similar fashion, we explain why some wellknown spatiotemporal systems have
been found to produce very complex dynamics in numerical simulations. We
discuss real physical systems that can generate random dynamics.Comment: Accepted in International Journal of Bifurcation and Chao
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