Synchronizing strict-feedback chaotic system via a scalar driving signal

We propose a systematic design procedure to synchronize a class of chaotic system in a so-called strict-feedback form based on back-stepping procedure. This approach needs only a scalar driving signal to realize synchronization no matter how many dimensions the chaotic system contains. Furthermore, the numerical simulation with Chua's chaotic circuit verifies the effectiveness of the method.     

Synchronizing multiple chaotic maps with a randomized scalar coupling

Synchronization between chaotic systems has recently been a topic of great interest among physicists and engineers. In addition to theoretical results, a number of applications in communications and control have also been proposed. We have previously shown that identical chaotic maps can, under certain conditions, be synchronized by a common noise-like input. This raises the question whether the chaotic output from a map can synchronize other maps to itself. In this paper, we present results on the synchronization of two identical maps where the output of one map is used to drive both maps. We then apply this method to synchronizing identical but internally inhomogeneous populations of chaotic oscillators using a randomly constructed scalar coupling signal, which tends to white noise as the number of oscillators increases. Such a system may have applications in secure communication.     

间歇性正比于系统变量方法控制超混沌的实验

利用电子电路和PSPICE软件实现了间歇性正比于系统变量方法控制超混沌的实验，在实验中进一步拓展间歇性正比于系统变量方法，用一个微扰反馈信号作用到系统的其它变量，得到了较好的控制效果。     

Synchronizing a chaotic laser by injecting a chaotic signal with a frequency offset

It has been theoretically proven that a chaotic laser driven by an injected signal derived from a similar chaotic master oscillator working at a slight frequency offset operates in a new mode of synchronization. There is a certain relationship between average laser fields, which has been approximately calculated in an explicit form, and instantaneous fields form an attractor about the point defined by these average values, with a relatively small spread in the phase trajectories around it. It has been shown that such a configuration can be used in transmitting confidential information. Zh. éksp. Teor. Fiz. 115, 1593–1604 (May 1999)     

控制超混沌的电路实验

基于限幅法控制混沌的原理，设计了一个控制超混沌的实验电路，采用单限幅的方式，得到了被稳定住的不同的周期轨道，同时进行了数值模拟计算，模拟结果与实验结果相吻合。     

Hyperchaotic behaviours and controlling hyperchaos in an array of RCL-shunted Josephson junctions

This paper deals with dynamical behaviours in an array composed of two resistive-capacitive-inductive-shunted (RCL-shunted) Josephson junctions (RCLSJJs) and a shunted resistor. Numerical simulations show that periodic, chaotic and hyperchaotic states can coexist in this array. Moreover, a scheme for controlling hyperchaos in this array is presented by adjusting the external bias current. Numerical results confirm that this scheme can be effectively used to control hyperchaotic states in this array into stable periodic states, and different stable periodic states with different period numbers can be obtained by appropriately choosing the intensity of the external bias current.     

一种控制掺铒光纤激光器超混沌的方法——非线性延时反馈参数调制法

提出一种非线性延时反馈参数调制法来控制混沌/超混沌，给出了利用这种方法控制处于超混沌状态的双环掺铒光纤激光器的方案.数值模拟表明，只要延时时间和反馈强度合适就可以把双环掺铒光纤激光器从超混沌状态成功地控制到不同的周期状态. 关键词： 掺铒光纤激光器 超混沌 非线性延时反馈参数调制 混沌控制     

Interpolation parameter and expansion for a three-dimensional nontrivial scalar infrared fixed point

We compute a nontrivial infraredϕ ₃ ⁴ -fixed point by means of an interpolation expansion in fixed dimension. The expansion is formulated for an infinitesimal momentum-space renormalization group. We choose a coordinate representation for the fixed-point interaction in derivative expansion, and compute its coordinates to high orders by means of computer algebra. We compute the series for the critical exponentv up to order 25 of interpolation expansion in this representation, and evaluate it using Padé, Borel-Padé, Borel-conformal-Padé, andD log -Padé resummation. The resummation returns 0.6262(13) as the value ofv. Our renormalization group uses canonical resealing, for whichη = 0     

Chaos and hyperchaos in a gyrotron

We study oscillation in a gyrotron with allowance for reflections from an output horn. Regions with different system behaviors, such as stationary oscillation, self-modulation, and complex-dynamics regimes are found in the parameter plane. The scenarios of appearance of chaotic oscillations are considered. It is shown that they can emerge via either a sequence of period-doubling bifurcations or destruction of quasiperiodic motion. For chaotic attractors, Lyapunov exponents are calculated and their dimensions are estimated on the basis of the Kaplan-Yorke formula. The dimension values turn out to be anomalously large, which is stipulated by the presence of a large number of high-Q eigenmodes in the gyrotron cavity due to operation near the cutoff frequency of an electrodynamic system. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 49, No. 10, pp. 887–899, October 2006.     

The possibility of controlling the optical limiting effect by a weak light signal

When investigating the nonlinear transmission of fullerene-doped π-conjugate organic structures, it has been found for the first time that the broad-band light of a flashlamp has considerable impact on the optical limiting of infrared laser emission (λ=1315 nm).     

A new output feedback synchronization theorem for a class of chaotic systems with a scalar transmitted signal

This paper proposes a new, simple and yet applicable output feedback synchronization theorem for a large class of chaotic systems. We take a linear combination of drive system state variables as a scale-driving signal. It is proved that synchronization between the drive and the response systems can be obtained via a simple linear output error feedback control. The linear feedback gain is a function of a free parameter. The approach is illustrated using the R\"{o}ssler hyperchaotic systems and Chua's chaotic oscillators.     

Memristor hyperchaos in a generalized Kolmogorov-type system with extreme multistability

Memristor chaotic systems have aroused great attention in recent years with their potentials expected in engineering applications. In this paper, a five-dimension (5D) double-memristor hyperchaotic system (DMHS) is modeled by introducing two active magnetron memristor models into the Kolmogorov-type formula. The boundness condition of the proposed hyperchaotic system is proved. Coexisting bifurcation diagram and numerical verification explain the bistability. The rich dynamics of the system are demonstrated by the dynamic evolution map and the basin. The simulation results reveal the existence of transient hyperchaos and hidden extreme multistability in the presented DMHS. The NIST tests show that the generated signal sequence is highly random, which is feasible for encryption purposes. Furthermore, the system is implemented based on a FPGA experimental platform, which benefits the further applications of the proposed hyperchaos.     

Traffic behavior in the on-ramp system with signal controlling

In this paper, we investigate the on-ramp system on the highway using cellular automaton traffic model. Different from previous work, we introduce traffic signal to control the vehicle flows on the main road and the on-ramp. A method of signal controlling is presented, and the update rule in special road is given in detail according to the stimulation role of signal to the drivers. The simulation results show that, the phase diagram of on-ramp system is divided into three regions. The currents of the on-ramp system are discussed. Under the control role of traffic signal, the vehicle flows of the main road and the on-ramp can become orderly. The capacity of the system may keep a maximum value. In addition, the drastic velocity fluctuation is discussed near the on-ramp. A dangerous condition in Jiang et al. [Phys. Rev. E 66 (2002) 036104] can be effectively avoided.     

Synchronization of chaotic VCSELs by external chaotic signal parameter modulation

Synchronization of chaotic vertical-cavity surface-emitting lasers （VCSELs） is achieved by external chaotic signal modulation successfully. Simulation indicates that we can get chaos synchronization if the intensity of external chaotic signal is large enough. First of all, we use direct current modulation to achieve the chaos of VCSELs, and determine the laser＇s chaotic state by analyzing time series of the output and the corresponding power spectrum. And then we achieve synchronization of the two chaotic systems by external chaotic signal parameter modulation. We also find that the larger the modulation intensity is, the easier it is to achieve synchronization for chaotic VCSELs. This approach can also be applied to systems with a number of modulated lasers.     

A novel hyperchaos system only with one equilibrium

This Letter presents a new hyperchaotic system by introducing an additional state feedback into a three-dimensional quadratic chaotic system. The system only has one equilibrium, but it can evolve into periodic, quasi-periodic, chaotic and hyperchaotic dynamical behaviors. Basic bifurcation analysis of the new system is investigated by means of Lyapunov exponent spectrum and bifurcation diagrams. We find that the new hyperchaotic system possesses two big positive Lyapunov exponents within a large range of parameters. Therefore, the new hyperchaotic system may have good application prospects.     

Arbitrary full-state hybrid projective synchronization for chaotic discrete-time systems via a scalar signal

In this paper we present a new projective synchronization scheme,where two chaotic(hyperchaotic) discretetime systems synchronize for any arbitrary scaling matrix.Specifically,each drive system state synchronizes with a linear combination of response system states.The proposed observer-based approach presents some useful features:i) it enables exact synchronization to be achieved in finite time(i.e.,dead-beat synchronization);ii) it exploits a scalar synchronizing signal;iii) it can be applied to a wide class of discrete-time chaotic(hyperchaotic) systems;iv) it includes,as a particular case,most of the synchronization types defined so far.An example is reported,which shows in detail that exact synchronization is effectively achieved in finite time,using a scalar synchronizing signal only,for any arbitrary scaling matrix.