205 research outputs found
Mixing and relaxation dynamics of the Henon map at the edge of chaos
The mixing properties (or sensitivity to initial conditions) and relaxation
dynamics of the Henon map, together with the connection between these concepts,
have been explored numerically at the edge of chaos. It is found that the
results are consistent with those coming from one-dimensional dissipative maps.
This constitutes the first verification of the scenario in two-dimensional
cases and obviously reinforces the idea of weak mixing and weak chaos.
Keywords: Nonextensive thermostatistics, Henon map, dynamical systemsComment: 10 pages with 3 fig
Damage spreading in 2-dimensional isotropic and anisotropic Bak-Sneppen models
We implement the damage spreading technique on 2-dimensional isotropic and
anisotropic Bak-Sneppen models. Our extensive numerical simulations show that
there exists a power-law sensitivity to the initial conditions at the
statistically stationary state (self-organized critical state). Corresponding
growth exponent for the Hamming distance and the dynamical exponent
are calculated. These values allow us to observe a clear data collapse of
the finite size scaling for both versions of the Bak-Sneppen model. Moreover,
it is shown that the growth exponent of the distance in the isotropic and
anisotropic Bak-Sneppen models is strongly affected by the choice of the
transient time.Comment: revised version, 9 pages, 5 eps figures, use of svjour.st
Dissipative maps at the chaos threshold: Numerical results for the single-site map
We numerically study, at the edge of chaos, the behaviour of the sibgle-site
map , where is the map parameter.Comment: 8 pages with 4 figures, submitted to Physica
Asymmetric Unimodal Maps: Some Results from q-generalized Bit Cumulants
In this study, using q-generalized bit cumulants (q is the nonextensivity
parameter of the recently introduced Tsallis statistics), we investigate the
asymmetric unimodal maps. The study of the q-generalized second cumulant of
these maps allows us to determine, for the first time, the dependence of the
inflexion paremeter pairs (z_1,z_2) to the nonextensivity parameter q. This
behaviour is found to be very similar to that of the logistic-like maps
(z_1=z_2=z) reported recently by Costa et al. [Phys.Rev.E 56 (1997) 245].Comment: 6 pages with 3 fig
Sensitivity function and entropy increase rates for z-logistic map family at the edge of chaos
It is well known that, for chaotic systems, the production of relevant
entropy (Boltzmann-Gibbs) is always linear and the system has strong
(exponential) sensitivity to initial conditions. In recent years, various
numerical results indicate that basically the same type of behavior emerges at
the edge of chaos if a specific generalization of the entropy and the
exponential are used. In this work, we contribute to this scenario by
numerically analysing some generalized nonextensive entropies and their related
exponential definitions using -logistic map family. We also corroborate our
findings by testing them at accumulation points of different cycles.Comment: 9 pages, 2 fig
Two-dimensional maps at the edge of chaos: Numerical results for the Henon map
The mixing properties (or sensitivity to initial conditions) of
two-dimensional Henon map have been explored numerically at the edge of chaos.
Three independent methods, which have been developed and used so far for the
one-dimensional maps, have been used to accomplish this task. These methods are
(i)measure of the divergence of initially nearby orbits, (ii)analysis of the
multifractal spectrum and (iii)computation of nonextensive entropy increase
rates. The obtained results strongly agree with those of the one-dimensional
cases and constitute the first verification of this scenario in two-dimensional
maps. This obviously makes the idea of weak chaos even more robust.Comment: 4 pages, 3 figure
Generalized Huberman-Rudnick scaling law and robustness of -Gaussian probability distributions
We generalize Huberman-Rudnick universal scaling law for all periodic windows
of the logistic map and show the robustness of -Gaussian probability
distributions in the vicinity of chaos threshold. Our scaling relation is
universal for the self-similar windows of the map which exhibit period-doubling
subharmonic bifurcations. Using this generalized scaling argument, for all
periodic windows, as chaos threshold is approached, a developing convergence to
-Gaussian is numerically obtained both in the central regions and tails of
the probability distributions of sums of iterates.Comment: 13 pages, 3 figure
Damage spreading in the Bak-Sneppen model: Sensitivity to the initial conditions and equilibration dynamics
The short-time and long-time dynamics of the Bak-Sneppen model of biological
evolution are investigated using the damage spreading technique. By defining a
proper Hamming distance measure, we are able to make it exhibits an initial
power-law growth which, for finite size systems, is followed by a decay towards
equilibrium. In this sense, the dynamics of self-organized critical states is
shown to be similar to the one observed at the usual critical point of
continuous phase-transitions and at the onset of chaos of non-linear
low-dimensional dynamical maps. The transient, pre-asymptotic and asymptotic
exponential relaxation of the Hamming distance between two initially
uncorrelated equilibrium configurations is also shown to be fitted within a
single mathematical framework. A connection with nonextensive statistical
mechanics is exhibited.Comment: 6 pages, 4 figs, revised version, accepted for publication in
Int.J.Mod.Phys.C 14 (2003
Convergence dynamics of 2-dimensional isotropic and anisotropic Bak-Sneppen models
The conventional Hamming distance measurement captures only the short-time
dynamics of the displacement between the uncorrelated random configurations.
The minimum difference technique introduced by Tirnakli and Lyra [Int. J. Mod.
Phys. C 14, 805 (2003)] is used to study the short-time and long-time dynamics
of the two distinct random configurations of the isotropic and anisotropic
Bak-Sneppen models on a square lattice. Similar to 1-dimensional case, the time
evolution of the displacement is intermittent. The scaling behavior of the jump
activity rate and waiting time distribution reveal the absence of typical
spatial-temporal scales in the mechanism of displacement jumps used to quantify
the convergence dynamics.Comment: 7 pages, 4 eps figures, 1 bbl fil
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