Synchronization in the network of chaotic microwave oscillators

Time scale synchronization in networks of chaotic microwave oscillators with the different topologies of the links between nodes has been studied. As a node element of the network the one-dimensional distributed model of the low-voltage vircator has been used. To characterize the degree of synchronization in the whole network the synchronization index has been introduced. The transition to the synchronous regime is shown to take place via cluster time scale synchronization. Meanwhile, the spectral structure of the output signals is complicated sufficiently which allows using such devices in a number of practical applications.     

Chaotic synchronization in coupled spatially extended beam–plasma systems

The appearance of the chaotic synchronization regimes has been discovered for the coupled spatially extended beam–plasma Pierce systems. The coupling was introduced only on the right bound of each subsystem. It has been shown that with coupling increase the spatially extended beam–plasma systems show the transition from asynchronous behavior to the phase synchronization and then to the complete synchronization regime. For the consideration of the chaotic synchronization we used the concept of time-scale synchronization described in work [A.E. Hramov, A.A. Koronovskii, Chaos 14 (3) (2004) 603] and based on the introduction of the continuous set of phases of chaotic signal. In case of unidirectional coupling the generalized synchronization regime has been observed in the spatially extended beam–plasma systems. The generalized synchronization appearance mechanism has been analyzed by means of the offered modified system approach [A.E. Hramov, A.A. Koronovskii, Phys. Rev. E 71 (6) (2005) 067201].     

Synchronous behavior of coupled systems with discrete time

The dynamics of one-way coupled systems with discrete time is considered. The behavior of the coupled logistic maps is compared to the dynamics of maps obtained using the Poincaré sectioning procedure applied to the coupled continuous-time systems in the phase synchronization regime. The behavior (previously considered as asynchronous) of the coupled maps that appears when the complete synchronization regime is broken as the coupling parameter decreases, corresponds to the phase synchronization of flow systems, and should be considered as a synchronous regime. A quantitative measure of the degree of synchronism for the interacting systems with discrete time is proposed.     

Frequency domain analysis of the chaotic synchronization of injection-locked semiconductor lasers

The quality and degree of synchronization obtained between a chaotic master laser diode and a slave laser diode is usually assessed using a correlogram. This technique is known to accurately identify areas of good synchronization, but it is not able to elucidate why these regions exist. By using a complementary frequency domain technique, the response gain, we have been able to obtain further insight into the synchronization process. We show using numerical simulations that trends in synchronization quality evident in the injection-locking diagram are also present in the response gain. We also show that most of the spectral power is situated in a small band of frequencies close to the relaxation oscillation frequency of the master laser and that accurate reproduction of these frequency components in the slave laser is vital in achieving a good synchronization. We associate the variation in synchronization quality within the injection-locking regime to changes in the response gain profile induced by the optical injection from the master laser. Variations in the spectral profile of the response gain clearly delineate and explain the various regions seen in the correlation synchronization diagram.     

Dual-lag synchronization between coupled chaotic lasers due to path-delay interference

We study experimentally the synchronization dynamics of two semiconductor lasers coupled unidirectionally via two different delayed paths. The emitter laser operates in a chaotic regime characterized by low-frequency fluctuations due to optical feedback and induces a synchronized dynamical activity in the receiver laser, which operates in the continuous-wave regime when uncoupled. Different delays in the two coupling paths lead to the coexistence of two time lags in the synchronized dynamics of the oscillators. This dual-lag synchronization degrades the average synchronization quality of the system of coupled lasers and hinders the transmission of information between them. Numerical simulation results agree with the experimental observations, and allow us to explore this phenomenon in a wide parameter range, and quantify the degree of signal transmission degradation caused by this chaotic path-delay interference.     

On the influence of spatial hole-burning on mode selection and mode synchronization in a CW laser

The influence of spatial saturation modulation of both the amplifier and absorber in a laser with a Fabry-Perot resonator, and of the associated Bragg-reflection, on the frequency-dependent losses necessary for single-frequency operation, as well as on the frequency synchronization of three modes, has been examined. Conditions for mode selection and mode synchronization are given. To achieve single-frequency operation in a laser with a Fabry-Perot resonator the loss difference between the mode to be selected and modes to be quenched has to be proportional to the Bragg losses of the selected mode suffered by its self-induced grating. The proportionality factor depends on the length and position of the amplifier in the cavity. In the case of a short amplifier and a short absorber inside the resonator, the discussion of conditions for synchronization of three modes shows that the synchronization regime is also determined by the position of the absorber.     

Forced synchronization of a delayed-feedback oscillator

Dynamics of a delayed-feedback oscillator with cubic nonlinearity driven by an external harmonic signal is considered. Regimes of forced synchronization and their stability conditions are studied analytically and numerically for the cases of single-frequency and multiple-frequency (self-modulation) operation of the free-running oscillator. Special attention is paid to synchronization of the oscillator with bistability of steady states which arises near the boundary of generation zone. Results of numerical simulation of bifurcation transitions to synchronization regime for different driving frequencies are presented. Main differences from the classical picture of synchronization for a system with one degree of freedom are discussed.     

Practical time-delay synchronization of a periodically modulated self-excited oscillators with uncertainties

This paper studies time-delay synchronization of a periodically modulated Duffing Van der Pol (DVP) oscillator subjected to uncertainties with emphasis on complete synchronization. A robust adaptive response system is designed to synchronize with the uncertain drive periodically modulated DVP oscillator. Adaptation laws on the upper bounds of uncertainties are proposed to guarantee the boundedness of both the synchronization error and the estimated feedback coupling gains. Numerical results are presented to check the effectiveness of the proposed synchronization scheme. The results suggest that the linear and nonlinear terms in the feedback coupling play a complementary role in increasing the synchronization regime in the parameter space of the synchronization manifold. The proposed method can be successfully applied to a large variety of physical systems.     

Phase Synchronization of Coupled Rossler Oscillators: Amplitude Effect

Phase synchronization of two linearly coupled Rossler oscillators with parameter misfits is explored.It is found that depending on parameter mismatches,the synchronization of phases exhibits different manners.The synchronization regime can be divided into three regimes.For small mismatches,the amplitude-insensitive regime gives the phase-dominant synchronization; When the parameter misfit increases,the amplitudes and phases of oscillators are correlated,and the amplitudes will dominate the synchronous dynamics for very large mismatches.The lag time among phases exhibits a power law when phase synchronization is achieved.     

Analysis of phase synchronization of chaotic oscillations in terms of symbolic CTQ-analysis

The application of symbolic CTQ-analysis for studying synchronization of chaotic oscillations is considered. This approach differs substantially from its analogs since it makes it possible to diagnose and measure quantitatively the characteristics of intermittency regimes in synchronization of chaotic systems and, hence, to analyzer the temporal structure of synchronization. The application of the symbolic analysis apparatus based on the T alphabet to systems with phase locking and synchronization of time scales is demonstrated for the first time. As an example, a complex system of two mutually coupled nonidentical Rössler oscillators in the helical chaos regime with attractors having an ill-conditioned phase is considered. The results show that the method considered here makes it possible to reliably diagnose synchronism sooner than a phase locking and/or time-scale synchronization threshold is detected.     

Complete and phase synchronization in a heterogeneous small-world neuronal network

Synchronous firing of neurons is thought to be important for information communication in neuronal networks. This paper investigates the complete and phase synchronization in a heterogeneous small-world chaotic Hindmarsh--Rose neuronal network. The effects of various network parameters on synchronization behaviour are discussed with some biological explanations. Complete synchronization of small-world neuronal networks is studied theoretically by the master stability function method. It is shown that the coupling strength necessary for complete or phase synchronization decreases with the neuron number, the node degree and the connection density are increased. The effect of heterogeneity of neuronal networks is also considered and it is found that the network heterogeneity has an adverse effect on synchrony.     

Experimental investigation on synchronization of three co-rotating non-identical coupled exciters driven by three motors

This work is a continuation and verification of the original literature by means of experiment. According to the previously published paper, the criteria of synchronization and stability for three co-rotating three exciters in an analytical form, as well as their numerical results, are directly provided. A synchronization experiment with three exciters is carried out. The experimental data on phase differences, rotational velocities, system responses, coupling torques, and so on, are quantitatively discussed by dividing the operational processes of the system into four stages. The coupling torques, which are the key determining factors for implementing synchronization, are particularly examined to explain the synchronization regime, based on the average energy method. The quality of synchronization is provided, and the noise and uncertainties in the experimental data are analyzed. It is shown that the experimental results obtained concur with the theoretical results.     

Paths to synchronization on complex networks

The understanding of emergent collective phenomena in natural and social systems has driven the interest of scientists from different disciplines during decades. Among these phenomena, the synchronization of a set of interacting individuals or units has been intensively studied because of its ubiquity in the natural world. In this Letter, we show how for fixed coupling strengths local patterns of synchronization emerge differently in homogeneous and heterogeneous complex networks, driving the process towards a certain global synchronization degree following different paths. The dependence of the dynamics on the coupling strength and on the topology is unveiled. This study provides a new perspective and tools to understand this emerging phenomena.     

Establishing generalized synchronization in Rössler oscillator networks

The processes of establishing of generalized chaotic synchronization in a network of mutually coupled continuous-time systems are investigated. The nature of interaction between the network elements in transitioning from synchronous to asynchronous behavior while increasing the communication parameter is studied. A synchronization regime, the nearest neighbors method, and calculations of the spectrum of Lyapunov exponents are used to clarify features of the interaction between network elements and the occurrence of a generalized chaotic.     

Weak and strong generalized chaotic synchronization

The existing concept of the weak and strong synchronization in discrete maps is verified. The state vectors of interacting chaotic systems are shown to be related to each other by the functional relation only in the strong synchronization regime; in the weak regime, the prehistory must be taken into account. An approach to determining the threshold of generalized synchronization in such systems is proposed.     

On electric-pulse well drilling and breaking of solids

Research work has been carried out to determine the power-efficient regime of operation of an electric-pulse setup for breaking and crushing natural stones. The optimal energy and geometrical parameters of the method (dependence of the degree of breakdown of materials on the voltage and the electrode spacing in the switching unit) have been established. The proposed method makes it possible to effectively perform drilling in vertical wells for installing heat exchangers of thermal pumps.     

Phase switching in Hindmarsh-Rose relay neurons

A system of Hindmarsh-Rose relay neurons with time delay coupling is considered in which the relay (central) neuron has an additional feedback term that represents the interaction activity with a local environment. The strength of environmental coupling with the central neuron plays an important role in inducing synchronization and de-synchronization between the outer neurons. The strength of feedback developed from the environmental coupling has created a gradual quenching in the oscillations of the central neuron. At a higher feedback coupling strength, oscillation of the central neuron is suppressed drastically and a transition from a regime of synchronization to out-of-phase synchronization take place between the oscillations of the two outer neurons.     

Study on phase synchronization of stochastic chaotic system

This paper detects and characterizes the diverse roles played by bounded noise in chaotic phase synchronization (CPS) of weakly coupled nonlinear stochastic systems. Analysis of a paradigmatic model of two bidirectional coupled three-level food chains is carried out by various statistical measures such as Shannon entropy and mutual information. The results indicate that inside the synchronous regime, CPS is considerably reduced under the influence of bounded noise; near the onset of phase synchronization, temporal phase locking is diversely changed with the increase of noise, i.e., either weak or strong noise also degrades the degree of CPS, while intermediate noise enhances CPS remarkably, and an optimal noise intensity is detected that maximizes the enhancement.     

Role of unstable periodic orbits in phase and lag synchronization between coupled chaotic oscillators

An increase of the coupling strength in the system of two coupled R?ssler oscillators leads from a nonsynchronized state through phase synchronization to the regime of lag synchronization. The role of unstable periodic orbits in these transitions is investigated. Changes in the structure of attracting sets are discussed. We demonstrate that the onset of phase synchronization is related to phase-lockings on the surfaces of unstable tori, whereas transition from phase to lag synchronization is preceded by a decrease in the number of unstable periodic orbits.