13,235 research outputs found
Composite "zigzag" structures in the 1D complex Ginzburg-Landau equation
We study the dynamics of the one-dimensional complex Ginzburg Landau equation
(CGLE) in the regime where holes and defects organize themselves into composite
superstructures which we call zigzags. Extensive numerical simulations of the
CGLE reveal a wide range of dynamical zigzag behavior which we summarize in a
`phase diagram'. We have performed a numerical linear stability and bifurcation
analysis of regular zigzag structures which reveals that traveling zigzags
bifurcate from stationary zigzags via a pitchfork bifurcation. This bifurcation
changes from supercritical (forward) to subcritical (backward) as a function of
the CGLE coefficients, and we show the relevance of this for the `phase
diagram'. Our findings indicate that in the zigzag parameter regime of the
CGLE, the transition between defect-rich and defect-poor states is governed by
bifurcations of the zigzag structures.Comment: 20 pages, 11 figure
Secure Communication Based on Hyperchaotic Chen System with Time-Delay
This research is partially supported by National Natural Science Foundation of China (61172070, 60804040), Fok Ying Tong Education Foundation Young Teacher Foundation(111065), Innovative Research Team of Shaanxi Province(2013KCT-04), The Key Basic Research Fund of Shaanxi Province (2016ZDJC-01), Chao Bai was supported by Excellent Ph.D. research fund (310-252071603) at XAUT.Peer reviewedPostprin
Energetics, skeletal dynamics and long-term predictions in Kolmogorov-Lorenz systems
We study a particular return map for a class of low dimensional chaotic
models called Kolmogorov Lorenz systems, which received an elegant general
Hamiltonian description and includes also the famous Lorenz63 case, from the
viewpoint of energy and Casimir balance. In particular it is considered in
detail a subclass of these models, precisely those obtained from the Lorenz63
by a small perturbation on the standard parameters, which includes for example
the forced Lorenz case in Ref.[6]. The paper is divided into two parts. In the
first part the extremes of the mentioned state functions are considered, which
define an invariant manifold, used to construct an appropriate Poincare surface
for our return map. From the experimental observation of the simple orbital
motion around the two unstable fixed points, together with the circumstance
that these orbits are classified by their energy or Casimir maximum, we
construct a conceptually simple skeletal dynamics valid within our sub class,
reproducing quite well the Lorenz map for Casimir. This energetic approach
sheds some light on the physical mechanism underlying regime transitions. The
second part of the paper is devoted to the investigation of a new type of
maximum energy based long term predictions, by which the knowledge of a
particular maximum energy shell amounts to the knowledge of the future
(qualitative) behaviour of the system. It is shown that, in this respect, a
local analysis of predictability is not appropriate for a complete
characterization of this behaviour. A perspective on the possible extensions of
this type of predictability analysis to more realistic cases in (geo)fluid
dynamics is discussed at the end of the paper.Comment: 21 pages, 14 figure
Grid multi-wing butterfly chaotic attractors generated from a new 3-D quadratic autonomous system
Due to the dynamic characteristics of the Lorenz system, multi-wing chaotic systems are still confined in the positive half-space and fail to break the threshold limit. In this paper, a new approach for generating complex grid multi-wing attractors that can break the threshold limit via a novel nonlinear modulating function is proposed from the firstly proposed double-wing chaotic system. The proposed method is different from that of classical multi-scroll chaotic attractors generated by odd-symmetric multi-segment linear functions from Chua system. The new system is autonomous and can generate various grid multi-wing butterfly chaotic attractors without requiring any external forcing, it also can produce grid multi-wing both on the xz-plane and yz-plane. Basic properties of the new system such as dissipation property, equilibrium, stability, the Lyapunov exponent spectrum and bifurcation diagram are introduced by numerical simulation, theoretical analysis and circuit experiment, which confirm that the multi-wing attractors chaotic system has more rich and complicated chaotic dynamics. Finally, a novel module-based unified circuit is designed which provides some principles and guidelines for future circuitry design and engineering application. The circuit experimental results are consistent with the numerical simulation results. 
New approach to the treatment of separatrix chaos and its application to the global chaos onset between adjacent separatrices
We have developed the {\it general method} for the description of {\it
separatrix chaos}, basing on the analysis of the separatrix map dynamics.
Matching it with the resonant Hamiltonian analysis, we show that, for a given
amplitude of perturbation, the maximum width of the chaotic layer in energy may
be much larger than it was assumed before. We apply the above theory to explain
the drastic facilitation of global chaos onset in time-periodically perturbed
Hamiltonian systems possessing two or more separatrices, previously discovered
(PRL 90, 174101 (2003)). The theory well agrees with simulations. We also
discuss generalizations and applications. Examples of applications of the
facilitation include: the increase of the DC conductivity in spatially periodic
structures, the reduction of activation barriers for noise-induced transitions
and the related acceleration of spatial diffusion, the facilitation of the
stochastic web formation in a wave-driven or kicked oscillator.Comment: 29 pages, 16 figures (figs. are of reduced quality, original files
are available on request from authors), paper has been significantly revised
and resubmitted to PR
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