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1.
Generalized reduced-order synchronization of chaotic system based on fast slide mode 总被引:1,自引:0,他引:1 下载免费PDF全文
A new kind of generalized reduced-order synchronization of different chaotic
systems is proposed in this paper. It is shown that dynamical evolution of
third-order oscillator can be synchronized with the canonical projection of
a fourth-order chaotic system generated through nonsingular states
transformation from a cell neural net chaotic system. In this sense, it is
said that generalized synchronization is achieved in reduced-order. The
synchronization discussed here expands the scope of reduced-order
synchronization studied in relevant literatures. In this way, we can achieve
generalized reduced-order synchronization between many famous chaotic
systems such as the second-order D\"{u}ffing system and the third-order
Lorenz system by designing a fast slide mode controller. Simulation results
are provided to verify the operation of the designed synchronization. 相似文献
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The notion of phase synchronization in time-delay systems, exhibiting highly non-phase-coherent attractors, has not been realized yet even though it has been well studied in chaotic dynamical systems without delay. We report the identification of phase synchronization in coupled nonidentical piecewise linear and in coupled Mackey-Glass time-delay systems with highly non-phase-coherent regimes. We show that there is a transition from nonsynchronized behavior to phase and then to generalized synchronization as a function of coupling strength. We have introduced a transformation to capture the phase of the non-phase-coherent attractors, which works equally well for both the time-delay systems. The instantaneous phases of the above coupled systems calculated from the transformed attractors satisfy both the phase and mean frequency locking conditions. These transitions are also characterized in terms of recurrence-based indices, namely generalized autocorrelation function P(t), correlation of probability of recurrence, joint probability of recurrence, and similarity of probability of recurrence. We have quantified the different synchronization regimes in terms of these indices. The existence of phase synchronization is also characterized by typical transitions in the Lyapunov exponents of the coupled time-delay systems. 相似文献
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In this paper, a bidirectional
partial generalized (lag, complete, and anticipated) synchronization
of a class of continuous-time systems is defined. Then based on the
active control idea, a new systematic and concrete scheme is developed to achieve bidirectional partial generalized (lag, complete, and anticipated) synchronization between two chaotic systems or between chaotic and hyperchaotic systems. With the help
of symbolic-numerical computation, we choose the modified Chua system, Lorenz system, and the hyperchaotic
Tamasevicius-Namajunas-Cenys system to illustrate the proposed
scheme. Numerical simulations are used to verify the effectiveness
of the proposed scheme. It is interesting that partial chaos
synchronization not only can take place between two chaotic systems,
but also can take place between chaotic and hyperchaotic systems. The proposed
scheme can also be extended to research bidirectional partial
generalized (lag, complete, and anticipated) synchronization between
other dynamical systems. 相似文献
6.
In an experimental investigation of the response of a chaotic system to a chaotic driving force, we have observed synchronization of chaos of the response system in the forms of generalized synchronization, phase synchronization, and lag synchronization to the driving signal. In this paper we compare the features of these forms of synchronized chaos and study their relations and physical origins. We found that different forms of chaotic synchronization could be interpreted as different stages of nonlinear interaction between the coupled chaotic systems. (c) 1998 American Institute of Physics. 相似文献
7.
Przemysaw Perlikowski Andrzej Stefaski Tomasz Kapitaniak 《Journal of sound and vibration》2008,318(1-2):329-340
We describe the relation between the complete, phase and generalized synchronization of the mechanical oscillators (response system) driven by the chaotic signal generated by the driven system. We identified the close dependence between the changes in the spectrum of Lyapunov exponents and a transition to different types of synchronization. The strict connection between the complete synchronization (imperfect complete synchronization) of response oscillators and their phase or generalized synchronization with the driving system (the (1:1) mode locking) is shown. We argue that the observed phenomena are generic in the parameter space and preserved in the presence of a small parameter mismatch. 相似文献
8.
We investigate the chaotic phase synchronization in a system of coupled bursting neurons in small-world networks. A transition to mutual phase synchronization takes place on the bursting time scale of coupled oscillators, while on the spiking time scale, they behave asynchronously. It is shown that phase synchronization is largely facilitated by a large fraction of shortcuts, but saturates when it exceeds a critical value. We also study the external chaotic phase synchronization of bursting oscillators in the small-world network by a periodic driving signal applied to a single neuron. It is demonstrated that there exists an optimal small-world topology, resulting in the largest peak value of frequency locking interval in the parameter plane, where bursting synchronization is maintained, even with the external driving. The width of this interval increases with the driving amplitude, but decrease rapidly with the network size. We infer that the externally applied driving parameters outside the frequency locking region can effectively suppress pathologically synchronized rhythms of bursting neurons in the brain. 相似文献
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Generalized synchronization of two unidirectionally coupled discrete stochastic dynamical systems 下载免费PDF全文
The existence of two kinds of generalized synchronization manifold in two unidirectionally coupled discrete stochastic dynamical systems is studied in this paper. When the drive system is chaotic and the modified response system collapses to an asymptotically stable equilibrium or asymptotically stable periodic orbit, under certain conditions, the existence of the generalized synchronization can be converted to the problem of a Lipschitz contractive fixed point or Schauder fixed point. Moreover, the exponential attractive property of generalized synchronization manifold is strictly proved. In addition, numerical simulations demonstrate the correctness of the present theory. The physical background and meaning of the results obtained in this paper are also discussed.%vspace1mm 相似文献
10.
In this paper, generalized synchronization of two
different chaotic dynamical systems is investigated. An active control is
adopted to construct a response system which synchronizes with a given drive
system for a function relation. Based on rigorous analysis, the error system
is asymptotically stable at the equilibrium. Numerical simulations
illustrate the effectiveness of the proposed theory. 相似文献
11.
Realization of generalized synchronization between different chaotic systems via scalar controller 下载免费PDF全文
In this paper, a very simple generalized synchronization method between
different chaotic systems is presented. Only a scalar controller is used in
this method. The method of obtaining the scalar controller from chaotic
systems is established. The sufficient and necessary condition of
generalized synchronization is obtained from a rigorous theory,
and the
sufficient and necessary condition of generalized synchronization is
irrelative to chaotic system itself. Theoretical analyses
and simulation results
show that the method established in this paper is effective. 相似文献
12.
利用光纤环长外腔光反馈半导体激光器产生了频谱平坦的宽带混沌激光,其对应的激光频谱可有效地隐藏外腔的谐振频率,增加了系统的保密性.通过单向耦合方式,将产生的混沌激光注入到另一个参数相近的半导体激光器中,实现了平坦宽带混沌同步输出,两同步激光器输出的相关系数达到084.同时实验研究了注入强度和主从激光器的频率失谐对同步质量的影响,结果表明在强光注入锁定下,在很大频率失谐范围内均可实现同步,而且注入强度越大,主从激光器输出的相关系数越大,维持混沌同步所允许的频率失谐范围越大.
关键词:
混沌同步
单向光纤环
光反馈
半导体激光器 相似文献
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In this paper, the chaotic generalized projective synchronization of a controlled, noised gyro with an expected gyro is investigated by a simple control law. Based on the theory of discontinuous dynamical systems, the necessary and sufficient conditions for such a synchronization are achieved. From such conditions, non-synchronization, partial and full synchronizations between the two coupled gyros are discussed. The switching scenarios between desynchronized and synchronized states of the two dynamical systems are shown. Numerical simulations are illustrated to verify the effectiveness of this method. 相似文献
16.
D. Hennequin P. Verkerk 《The European Physical Journal D - Atomic, Molecular, Optical and Plasma Physics》2010,57(1):95-104
The dynamics of cold atoms in conservative optical lattices obviously depends on the geometry of the lattice. But very similar
lattices may lead to deeply different dynamics. In a 2D optical lattice with a square mesh, it is expected that the coupling
between the degrees of freedom leads to chaotic motions. However, in some conditions, chaos remains marginal. The aim of this
paper is to understand the dynamical mechanisms inhibiting the appearance of chaos in such a case. As the quantum dynamics
of a system is defined as a function of its classical dynamics – e.g. quantum chaos is defined as the quantum regime of a
system whose classical dynamics is chaotic – we focus here on the dynamical regimes of classical atoms inside a well. We show
that when chaos is inhibited, the motions in the two directions of space are frequency locked in most of the phase space,
for most of the parameters of the lattice and atoms. This synchronization, not as strict as that of a dissipative system,
is nevertheless a mechanism powerful enough to explain that chaos cannot appear in such conditions. 相似文献
17.
Projective Synchronization in Drive--Response Networks via Impulsive Control 总被引:1,自引:0,他引:1 下载免费PDF全文
Impulsive projective synchronization in 1 +N coupled chaotic systems are investigated with the drive-response dynamical network (DRDN) model. Based on impulsive stability theory, some simple but less conservative criteria axe achieved for projective synchronization in DRDNs. Furthermore, impulsive pinning scheme is also adopted to direct the scaring factor onto the desired value. Numerical simulations on generalized chaotic unified system axe illustrated to verify the theoretical results. 相似文献
18.
G. Minero-Ramales D. López-Mancilla Carlos E. Castañeda G. Huerta Cuellar R. Chiu Z. J. Hugo García López R. Jaimes
Reátegui E. Villafaña Rauda C. Posadas-Castillo 《The European physical journal. Special topics》2016,225(13-14):2655-2667
This paper presents a novel electronic locking key based on discrete-time chaos synchronization. Two Chen chaos generators are synchronized using the Model-Matching Approach, from non-linear control theory, in order to perform the encryption/decryption of the signal to be transmitted. A model/transmitter system is designed, generating a key of chaotic pulses in discrete-time. A plant/receiver system uses the above mentioned key to unlock the mechanism. Two alternative schemes to transmit the private chaotic key are proposed. The first one utilizes two transmission channels. One channel is used to encrypt the chaotic key and the other is used to achieve output synchronization. The second alternative uses only one transmission channel for obtaining synchronization and encryption of the chaotic key. In both cases, the private chaotic key is encrypted again with chaos to solve secure communication-related problems. The results obtained via simulations contribute to enhance the electronic locking devices. 相似文献
19.
In this paper we investigate the synchronization problem of drive-response chaotic systems with a scalar coupling signal. By using the scalar transmitted signal from the drive chaotic system, an observer-based response chaotic system with dead-zone nonlinear input is designed. An output feedback control technique is derived to achieve generalized projective synchronization between the drive system and the response system. Furthermore, an adaptive control law is established that guarantees generalized projective synchronization without the knowledge of system nonlinearity, and/or system parameters as well as that of parameters in dead-zone input nonlinearity. Two illustrative examples are given to demonstrate the effectiveness of the proposed synchronization scheme. 相似文献
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In this paper, parameters of a given (chaotic) dynamical system are estimated from time series by using identical synchronization between two different systems. This technique is based on the invariance principle of differential equations, i.e., a dynamical Lyapunov function involving synchronization error and the estimation error of parameters. The control used in this synchronization consists of feedback and adaptive control loop associated with the update law of estimation parameters. Our estimation process indicates that one may identify dynamically all unknown parameters of a given (chaotic) system as long as time series of the system are available. Lorenz and Rossler systems are used to illustrate the validity of this technique. The corresponding numerical results and analysis on the effect of noise are also given. 相似文献