13 research outputs found
Fractal Properties of Robust Strange Nonchaotic Attractors in Maps of Two or More Dimensions
We consider the existence of robust strange nonchaotic attractors (SNA's) in
a simple class of quasiperiodically forced systems. Rigorous results are
presented demonstrating that the resulting attractors are strange in the sense
that their box-counting dimension is N+1 while their information dimension is
N. We also show how these properties are manifested in numerical experiments.Comment: 9 pages, 14 figure
Interruption of torus doubling bifurcation and genesis of strange nonchaotic attractors in a quasiperiodically forced map : Mechanisms and their characterizations
A simple quasiperiodically forced one-dimensional cubic map is shown to
exhibit very many types of routes to chaos via strange nonchaotic attractors
(SNAs) with reference to a two-parameter space. The routes include
transitions to chaos via SNAs from both one frequency torus and period doubled
torus. In the former case, we identify the fractalization and type I
intermittency routes. In the latter case, we point out that atleast four
distinct routes through which the truncation of torus doubling bifurcation and
the birth of SNAs take place in this model. In particular, the formation of
SNAs through Heagy-Hammel, fractalization and type--III intermittent mechanisms
are described. In addition, it has been found that in this system there are
some regions in the parameter space where a novel dynamics involving a sudden
expansion of the attractor which tames the growth of period-doubling
bifurcation takes place, giving birth to SNA. The SNAs created through
different mechanisms are characterized by the behaviour of the Lyapunov
exponents and their variance, by the estimation of phase sensitivity exponent
as well as through the distribution of finite-time Lyapunov exponents.Comment: 27 pages, RevTeX 4, 16 EPS figures. Phys. Rev. E (2001) to appea
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On the importance of the convergence to climate attractors
Ensemble approaches are becoming widely used in climate research. In contrast to weather forecast, however, in the climatic context one is interested in long-time properties, those arising on the scale of several decades. The well-known strong internal variability of the climate system implies the existence of a related dynamical attractor with chaotic properties. Under the condition of climate change this should be a snapshot attractor, naturally arising in an ensemble-based framework. Although ensemble averages can be evaluated at any instant of time, results obtained during the process of convergence of the ensemble towards the attractor are not relevant from the point of view of climate. In simulations, therefore, attention should be paid to whether the convergence to the attractor has taken place. We point out that this convergence is of exponential character, therefore, in a finite amount of time after initialization relevant results can be obtained. The role of the time scale separation due to the presence of the deep ocean is discussed from the point of view of ensemble simulations
Nonintegrable dynamics of the triplet-triplet spatiotemporal interaction
In this paper we examine the coupling of two wave triplets sharing two common modes. The analysis is performed in the solitonic sector of the parameter space where uncoupled solutions departing from linearly unstable homogeneous initial conditions evolve into a collection of regularly interspersed, spatiotemporally localized spikes. The uncoupled system is integrable, but coupling destroys integrability. As coupling grows, energy transfer to smaller spatial scales does appear and becomes faster not only in linearly unstable, but also in linearly stable cases. Chaos in low-dimensional subsystems appears to be responsible for the transfer. We perform a series of numerical tests to verify this idea
Pattern evolution in non-synchronizable scale-free networks
Pattern formation and evolution in the desynchronizing process of
scale-free complex networks are investigated. Depending on how far
the system is away from the synchronizable regime, two types of
synchronous patterns are identified, namely, the giant-cluster state
(GCS) and the scattered-cluster state (SCS). GCS is observed when a
system is immediately outside of the synchronizable regime, where
the dynamics undergoes a process of on-off intermittency and the
patterns are signatured by the existence of a giant synchronous
cluster. As the system leaves away from the synchronizable regime,
GCS gradually transforms into SCS, accompanied by the continuous
dissolving of the giant cluster. Both the two types of patterns are
non-stationary, reflected as the timely changed size and content of
the clusters. By introducing a new form of synchronization, the
temporal phase synchronization, we investigate the dynamical and
statistical properties of these non-stationary patterns. An
interesting finding is that the unstable nodes of GCS, i.e. nodes
that escape from the giant cluster more frequently, are independent
of the coupling strength but are sensitive to the bifurcation types.
The intermittent behavior of GCS is analyzed by a theory of snapshot
attractors, and the theoretical predications fit the numerical
observations qualitatively well