On computing the Lyapunov exponents of reversible cellular automata
نویسندگان
چکیده
منابع مشابه
Cellular automata and Lyapunov exponents
The first definition of Lyapunov exponents (depending on a probability measure) for a one-dimensional cellular automaton were introduced by Shereshevsky in 1991. The existence of an almost everywhere constant value for each of the two exponents (left and right), requires particular conditions for the measure. Shereshevsky establishes an inequality involving these two constants and the metric en...
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We study the synchronization of totalistic one dimensional cellular automata (CA). The CA with a non zero synchronization threshold exhibit complex non periodic space time patterns and conversely. This synchronization transition is related to directed percolation. We study also the maximum Lyapunov exponent for CA, defined in analogy with continuous dynamical systems as the exponential rate of ...
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Space-time directional Lyapunov exponents are introduced. They describe the maximal velocity of propagation to the right or to the left of fronts of perturbations in a frame moving with a given velocity. The continuity of these exponents as function of the velocity and an inequality relating them to the directional entropy is proved.
متن کاملSpace-time directional Lyapunov exponents for cellular automata
Space-time directional Lyapunov exponents are introduced. They describe the maximal velocity of propagation to the right or to the left of fronts of perturbations in a frame moving with a given velocity. The continuity of these exponents as function of the velocity and an inequality relating them to the directional entropy is proved.
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Cellular automata are mappings over infinite lattices such that each cell is updated according to the states around it and a unique local function. Block permutations are mappings that generalize a given permutation of blocks (finite arrays of fixed size) to a given partition of the lattice in blocks. We prove that any d-dimensional reversible cellular automaton can be expressed as the composit...
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ژورنال
عنوان ژورنال: Natural Computing
سال: 2020
ISSN: 1567-7818,1572-9796
DOI: 10.1007/s11047-020-09821-3