Generalized synchronization of two unidirectionally coupled discrete stochastic dynamical systems

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     

Phase synchronization in unidirectionally coupled Ikeda time-delay systems

Phase synchronization in unidirectionally coupled Ikeda time-delay systems exhibiting non-phase-coherent hyperchaotic attractors of complex topology with highly interwoven trajectories is studied. It is shown that in this set of coupled systems phase synchronization (PS)does exist in a range of the coupling strength which is preceded by a transition regime (approximate PS)and a nonsynchronous regime. However, exact generalized synchronization does not seem to occur in the coupled Ikeda systems (for the range of parameters we have studied)even for large coupling strength, in contrast to our earlier studies in coupled piecewise-linear and Mackey-Glass systems [27,28]. The above transitions are characterized in terms of recurrence based indices, namely generalized autocorrelation function P(t), correlation of probability of recurrence (CPR), joint probability of recurrence (JPR)and similarity of probability of recurrence (SPR). The existence of phase synchronization is also further confirmed by typical transitions in the Lyapunov exponents of the coupled Ikeda time-delay systems and also using the concept of localized sets.     

Synchronization of spectral components in unidirectionally coupled systems

The object of investigation is synchronization of spectral components in unidirectionally coupled chaotic systems. It is shown that the behavior of the spectral components in this case is governed by the amount of detuning between interacting systems. Universal laws of spectral component synchronization are discovered.     

Chaos synchronization and communication of the polarization modes for two unidirectionally coupled vertical-cavity surface-emitting lasers

We theoretically investigate the synchronization performance of the polarization modes of two unidirectionally coupled vertical-cavity surface-emitting lasers (VCSELs), where the master VCSEL subjects to polarization-preserved optical feedback and the slave VCSEL subjects to polarization-preserved optical injection. We demonstrate that high synchronization can be achieved between corresponding polarization components of the master laser and the slave laser. We also analyze the influence of the internal mismatched parameters on the synchronization performance. Furthermore, this system is used to dual-channel communication and the different transmitted digital information is respectively recovered at each polarization branch of the slaver laser successfully with the encryption scheme of chaos masking (CM). The results open an opportunity for multichannel chaotic communication by utilizing different polarization components in single-mode or multi-transverse-mode VCSELs.     

Effects of noise on the outer synchronization of two unidirectionally coupled complex dynamical networks

We study the effect of noise on the outer synchronization between two unidirectionally coupled complex networks and find analytically that outer synchronization could be achieved via white-noise-based coupling. It is also demonstrated that, if two networks have both conventional linear coupling and white-noise-based coupling, the critical deterministic coupling strength between two complex networks for synchronization transition decreases with an increase in the intensity of noise. We provide numerical results to illustrate the feasibility and effectiveness of the theoretical results.     

光电负反馈下单向耦合注入垂直腔表面发射激光器的混沌同步特性研究

基于自旋反转模型（SFM）,对光电负反馈下单向耦合注入垂直腔表面发射激光器（VCSEL）的混沌同步特性进行了数值仿真和理论分析.研究结果表明：随着反馈强度的增加,激光器输出功率呈现两个不同的混沌区域.在单一偏振模区域,能实现很好的同步性,但接近两模共存时,同步质量急剧下降;在两模共存区域,偏振模的连续性差,同步质量不理想.两模共存时的同步质量比单一偏振模差的这一特性,与已报道的基于光反馈的情景相反.产生这一特殊现象的原因是光电负反馈诱发了偏振模竞争效应.此外,还发现内部参数的变化对两个混沌区域的选取有较大 关键词： 线性偏振模 光电负反馈 垂直腔表面发射激光器（VCSEL） 混沌同步     

Influence of polarization mode competition on the synchronization of two unidirectionally coupled vertical-cavity surface-emitting lasers

We analyze theoretically the effect of polarization mode competition on the synchronization of two unidirectionally coupled vertical-cavity surface-emitting lasers (VCSELs). Chaos in the master laser is induced by delayed optical feedback, and the slave laser is subject to isotropic optical injection from the master VCSEL. We show that the synchronization quality can be enhanced when the chaotic regime in the master VCSEL involves both fundamental orthogonal linearly polarized modes.     

Transition to fully developed chaos in a system of two unidirectionally coupled backward-wave oscillators

The chaotic dynamics of a system of two unidirectionally coupled backward-wave oscillators (BWOs) is studied in the case when a signal from the driving BWO in (periodic or chaotic) self-modulation mode is applied to the driven oscillator, which exhibits strong periodic self-modulation in the autonomous case. The oscillation evolution with the amount of coupling is traced. The use of a chain of coupled BWOs is shown to significantly reduce the threshold of transition to the regime of wide-band chaotic oscillations with a uniform continuous spectrum (so-called fully developed chaos), which is of interest for applications.     

Real-space renormalization-group transformation for finite thickness ising systems

The real-space renormalization group transformation based on the cumulant expansion is modified for systems with free-surface boundary conditions. Free energies and heat capacities of ferromagnetic strips (n x ∞) and slabs (n x ∞ x ∞) are determined over a wide temperature range. The critical or pseudocritical behavior approaches the bulk limit as n → ∞ according to a simple power law, [T_c(n) ? T_c (∞)] ∞n^?λ it is verified that the shift exponent λ is equal to the reciprocal of the critical length exponent.     

Phase diagrams in unidirectionally coupled map lattice for open traffic flow

The jamming transition from the free traffic to the oscillatory traffic is investigated with the unidirectionally coupled map lattice model which has the hyperbolic tangent local map. Spatio-temporal structures in the jamming transition are found with the use of numerical simulation. The traffic states are studied for both constant and noisy boundary conditions. We show the phase diagrams of different kinds of congested traffic. It is found that the noise at the boundary has an important effect on the traffic states. The traffic behavior in the coupled map lattice model exhibits a jamming transition similar to that found in the car-following model.     

A bifurcation analysis of two coupled calcium oscillators

In many cell types, asynchronous or synchronous oscillations in the concentration of intracellular free calcium occur in adjacent cells that are coupled by gap junctions. Such oscillations are believed to underlie oscillatory intercellular calcium waves in some cell types, and thus it is important to understand how they occur and are modified by intercellular coupling. Using a previous model of intracellular calcium oscillations in pancreatic acinar cells, this article explores the effects of coupling two cells with a simple linear diffusion term. Depending on the concentration of a signal molecule, inositol (1,4,5)-trisphosphate, coupling two identical cells by diffusion can give rise to synchronized in-phase oscillations, as well as different-amplitude in-phase oscillations and same-amplitude antiphase oscillations. Coupling two nonidentical cells leads to more complex behaviors such as cascades of period doubling and multiply periodic solutions. This study is a first step towards understanding the role and significance of the diffusion of calcium through gap junctions in the coordination of oscillatory calcium waves in a variety of cell types. (c) 2001 American Institute of Physics.     

Synchronization of polarization mode of two unidirectionally coupled vertical-cavity surface-emitting laser and its application in communication

We theoretically investigate the synchronization performance of polarization mode of two unidirectionally coupled vertical-cavity surface-emitting laser (VCSEL) and propose an encryption scheme, where the phase of the polarization states of the master laser are modulated. It is demonstrated that high synchronization can be achieved between corresponding polarization components of the master laser and the slave laser. Moreover, two distinct synchronization regimes exist, complete synchronization and injection locking. The transmitted digital information is successfully recovered at each polarization branch of the slaver laser. The results open an opportunity for multichannel chaotic communication by utilizing different polarization components in single-mode or multi-transverse-mode VCSELs.     

A complete proof of the Feigenbaum conjectures

The Feigenbaum phenomenon is studied by analyzing an extended renormalization group map . This map acts on functions that are jointly analytic in a position variable (t) and in the parameter () that controls the period doubling phenomenon. A fixed point ^* for this map is found. The usual renormalization group doubling operatorN acts on this function ^* simply by multiplication of with the universal Feigenbaum ratio ^*= 4.669201..., i.e., (N ^*(,t)= ^*( ^* ,t). Therefore, the one-parameter family of functions, ^* , ^* (t)=( ^*(,t), is invariant underN. In particular, the function ₀ ^* is the Feigenbaum fixed point ofN, while ^* represents the unstable manifold ofN. It is proven that this unstable manifold crosses the manifold of functions with superstable period two transversally.     

A Migdal-Kadanoff renormalization-group approach for the XY spin glass

Superconducting rings with mesoscopic Josephson junctions are considered in the presence of a do voltage bias V _o and of non-classical electromagnetic fields (coherent states, squeezed states, number eigenstates etc.). Due to the quantum nature of these devices the current I is a quantum mechanical operator and therefore «I²» is in general different from «I»². Using «I ²» we define the rms current I _rms, and using the various harmonics of «I» as if they belong to a classical current we define the “classical rms current” I _{rms, class}. In the case of classical currents these two quantities are identical, but for quantum currents they are different. We study their difference for various non-classical fields, and find that in some cases this difference is large. These predictions could be observed experimentally through the electromagnetic power that these currents radiate. An experiment that confirms the I _rms and refutes the Irms, class would prove the quantum nature of these currents.