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1.
For the first time, we report on projective synchronization between two time delay chaotic systems with single time delays. It overcomes some limitations of the previous work, where projective synchronization has been investigated only in finite-dimensional chaotic systems, so we can achieve projective synchronization in infinitedimensional chaotic systems. We give a general method with which we can achieve projective synchronization in time-delayed chaotic systems. The method is illustrated using the famous delay-differential equations related to optical bistability. Numerical simulations fully support the analytical approach. 相似文献
2.
K. B. Blyuss Y. N. Kyrychko P. Hövel E. Schöll 《The European Physical Journal B - Condensed Matter and Complex Systems》2008,65(4):571-576
We present an analysis of time-delayed feedback control used to stabilize an unstable steady state of a neutral delay differential
equation. Stability of the controlled system is addressed by studying the eigenvalue spectrum of a corresponding characteristic
equation with two time delays. An analytic expression for the stabilizing control strength is derived in terms of original
system parameters and the time delay of the control. Theoretical and numerical results show that the interplay between thecontrol
strength and two time delays provides a number of regions in the parameter space where the time-delayed feedback control can
successfully stabilize an otherwise unstable steady state. 相似文献
3.
This Letter deals with the problem of designing time-delayed feedback controllers (TDFCs) to stabilize unstable equilibrium points and periodic orbits for a class of continuous time-delayed chaotic systems. Harmonic balance approach is used to select the appropriate controller parameters: delay time and feedback gain. The established theoretical results are illustrated via a case study of the well-known Logistic model. 相似文献
4.
Chaos synchronization and encoding in coupled semiconductor lasers of multiple modulated time delays
We numerically investigate the synchronization performance of unidirectionally and bidirectionally coupled chaotic semiconductor lasers subject to multiple modulated time delays optical feedbacks. Moreover, by studying the autocorrelation function of the coherent feedback semiconductor laser output, we find that the signatures of time delays can be erased in systems incorporating modulated feedback time delays, which largely improve the system security. Finally, chaos masking switching (CMS) is utilized to examine the communication ability. Numerical results indicate that the messages could be successfully recovered both in unidirectionally and bidirectionally coupled lasers, which confirms the possibility of applying multiple modulated delay system in optical chaos secure communication. 相似文献
5.
We report on chaos synchronization in both unidirectionally and bidirectionally coupled multiple time delay laser diodes with electro-optical feedback. We derive existence and sufficient stability conditions for the synchronization regimes. We calculate the Lyapunov exponents, information dimension, and Kolmogorov-Sinai entropy for a single and double delay time lasers to demonstrate that multiple time delay laser system can offer higher complexity than a single time delay laser. We demonstrate that in coupled multiple time delay lasers additional feedback(s) can play a stabilizing role. We compare the synchronization quality for closed loop and open loop receiver laser configurations and find better synchronization quality for partially open loop receiver (when the receiver laser has only one feedback loop), than the open loop receiver configuration (when the receiver contains no feedback loops). We also study the effect of the feedback phase on the correlation coefficient between the interacting laser systems. Analytical results are fully supported by numerical simulations. 相似文献
6.
A. Wilmer T. D. Frank P. J. Beek R. Friedrich 《The European Physical Journal B - Condensed Matter and Complex Systems》2007,60(2):203-215
In this work a method is developed for analyzing time series of
periodically driven stochastic systems involving time-delayed feedback.
The proposed data-analysis method yields
dynamical models in terms of stochastic delay differential equations. On
the basis of these dynamical models differential effects of driving
forces and time-delayed feedback forces can be identified. 相似文献
7.
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9.
Rui-Hua Shao 《Physica A》2009,388(6):977-983
We study theoretically a bistable system with time-delayed feedback driven by a weak periodic force. The effective potential function and the steady-state probability density are derived. The delay time and the strength of its feedback can change the shapes of the potential wells. In the adiabatic approximation, the signal-to-noise ratio (SNR) of the system with a weak periodic force is obtained. The time-delayed feedback modulates the magnitude of SNR by changing the shape of the potential and the effective strength of the signal. The maximum of SNR decreases with increasing the feedback intensity ?. When ? is negative (or positive), the time delay can suppress (or promote) the stochastic resonance phenomenon. 相似文献
10.
This Letter investigates the problem of synchronization in complex dynamical networks with time-varying delays. A periodically intermittent control scheme is proposed to achieve global exponential synchronization for a general complex network with both time-varying delays dynamical nodes and time-varying delays coupling. It is shown that the sates of the general complex network with both time-varying delays dynamical nodes and time-varying delays coupling can globally exponentially synchronize with a desired orbit under the designed intermittent controllers. Moreover, a typical network consisting of the time-delayed Chua oscillator with nearest-neighbor unidirectional time-varying delays coupling is given as an example to verify the effectiveness of the proposed control methodology. 相似文献
11.
We apply time-delayed feedback control to stabilise unstable periodic orbits of an amplitude-phase oscillator. The control acts on both, the amplitude and the frequency of the oscillator, and we show how the phase of the control signal influences the dynamics of the oscillator. A comprehensive bifurcation analysis in terms of the control phase and the control strength reveals large stability regions of the target periodic orbit, as well as an increasing number of unstable periodic orbits caused by the time delay of the feedback loop. Our results provide insight into the global features of time-delayed control schemes. 相似文献
12.
Dan Wu 《Physics letters. A》2008,372(32):5299-5304
The dynamics of a periodically driven FitzHugh-Nagumo system with time-delayed feedback and Gaussian white noise is investigated. The stochastic resonance which is characterized by the Fourier coefficient Q is numerically calculated. It is found that the stochastic resonance of the system is a non-monotonic function of the noise strength and the signal period. The variation of the time-delayed feedback can induce periodic stochastic resonance in the system. 相似文献
13.
M.J. Bünner M. Ciofini A. Giaquinta R. Hegger H. Kantz R. Meucci A. Politi 《The European Physical Journal D - Atomic, Molecular, Optical and Plasma Physics》2000,8(2):177-187
We apply a recently proposed method for the analysis of time series from systems with delayed feedback to experimental data
generated by a laser. The method allows estimating the delay time with an error of the order of the sampling interval, while an approach
based on the peaks of either the autocorrelation function, or the time delayed mutual information would yield systematically
larger values. We reconstruct rather accurately the equations of motion and, in turn, estimate the Lyapunov spectrum even
for high dimensional attractors. By comparing models constructed for different “embedding dimensions” with the original data,
we are able to find the minimal faithful model. For short delays, the results of our procedure have been cross-checked using
a conventional Takens time-delay embedding. For large delays, the standard analysis is inapplicable since the dynamics becomes
hyperchaotic. In such a regime we provide the first experimental evidence that the Lyapunov spectrum, rescaled according to
the delay time, is independent of the delay time itself. This is in full analogy with the independence of the system size
found in spatially extended systems.
Received 17 December 1999 相似文献
14.
We successfully demonstrated the first experimental stabilization of irregular and non-periodic cantilever oscillation in the amplitude modulation atomic force microscopy using the time-delayed feedback control. A perturbation to cantilever excitation force stabilized an unstable periodic orbit associated with nonlinear cantilever dynamics. Instead of the typical piezoelectric excitation, the magnetic excitation was used for directly applying control force to the cantilever. The control force also suppressed the cantilever's occasional bouncing motions that caused artifacts on a surface image. 相似文献
15.
In this Letter, we have dealt with the problem of lag synchronization and parameter identification for a class of chaotic neural networks with stochastic perturbation, which involve both the discrete and distributed time-varying delays. By the adaptive feedback technique, several sufficient conditions have been derived to ensure the synchronization of stochastic chaotic neural networks. Moreover, all the connection weight matrices can be estimated while the lag synchronization is achieved in mean square at the same time. The corresponding simulation results are given to show the effectiveness of the proposed method. 相似文献
16.
We establish two theorems for two time-delayed (chaotic) differential equation systems to achieve time-delayed generalized synchronization (TDGS). The theorems uncover general forms of two TDGS systems via a prescribed differentiable transformation. Based on the theorems, we use two-coupled Ikeda equations as the driving system to construct TDGS driven systems via two prescribed transformations. Numerical simulations demonstrate the effectiveness of the proposed theorems. It may be expected that our theorems provide new tools for understanding and studying TDGS phenomena. 相似文献
17.
Genera/dynamical networks with distributed time delays are studied. The topology of the networks are viewed as unknown parameters, which need to be identified. Some auxiliary systems (also called the network estimators) are designed to achieve this goal. Both linear feedback control and adaptive strategy are applied in designing these network estimators. Based on linear matrix inequalities and the Lyapunov function method, the sufficient condition for the achievement of topology identification is obtained. This method can also better monitor the switching topology of dynamical networks. Illustrative examples are provided to show the effectiveness of this method. 相似文献
18.
M.J. Bünner M. Ciofini A. Giaquinta R. Hegger H. Kantz R. Meucci A. Politi 《The European Physical Journal D - Atomic, Molecular, Optical and Plasma Physics》2000,10(2):165-176
High-dimensional chaos displayed by multi-component systems with a single time-delayed feedback is shown to be accessible
to time series analysis of a scalar variable only. The mapping of the original dynamics onto scalar time-delay systems defined
on sufficiently high dimensional spaces is thoroughly discussed. The dimension of the “embedding” space turns out to be independent
of the delay time and thus of the dimensionality of the attractor dynamics. As a consequence, the procedure described in the
present paper turns out to be definitely advantageous with respect to the standard embedding technique in the case of high-dimensional
chaos, when the latter is practically unapplicable. The mapping is not exact when delayed maps are used to reproduce the dynamics
of time-continuous systems, but the errors can be kept under control. In this context, the approximation of delay-differential
equations is discussed with reference to different classes of maps. Appropriate tools to estimate the a priori unknown delay time and the number of hidden components are introduced. The generalized Mackey-Glass system is investigated
in detail as a testing ground for the theoretical considerations.
Received 14 June 1999 and Received in final form 4 November 1999 相似文献
19.
The effects of time-delayed feedback control in a single-mode laser
system is investigated. Using the small time delay approximation,
the analytic expression of the stationary probability distribution
function of the laser field is obtained. The mean, normalized
variance and skewness of the steady-state laser intensity are
calculated. It is found that the time-delayed feedback control can
suppress the intensity fluctuation of the laser system. The
numerical simulations are in good agreement with the approximate
analytic results. 相似文献
20.
In this paper, a new method is presented to analyze the linear stability of the synchronized state in arbitrarily coupled complex dynamical systems with time delays. The coupling configurations are not restricted to the symmetric and irreducible connections or the non-negative off-diagonal links. The stability criteria are obtained by using Lyapunov-Krasovskii functional method and subspace projection method. These criteria reveal the relationship between coupling matrices and stability of the dynamical networks. 相似文献