Different Types Of Synchronization Research Articles

Forced synchronization of self-excited chaotic thermoacoustic oscillations

We experimentally investigate the forced synchronization of a self-excited chaotic thermoacoustic oscillator with two natural frequencies, $f_1$ and $f_2$ . On increasing the forcing amplitude, $\epsilon _f$ , at a fixed forcing frequency, $f_f$ , we find two different types of synchronization: (i) $f_f/f_1 = 1:1$ or $2:1$ chaos-destroying synchronization (CDS), and (ii) phase synchronization of chaos (PSC). En route to $1:1$ CDS, the system transitions from an unforced chaotic state ( ${\rm {CH}}_{1,2}$ ) to a forced chaotic state ( ${\rm {CH}}_{1,2,f}$ ), then to a two-frequency quasiperiodic state where chaos is destroyed ( $\mathbb {T}^2_{2,f}$ ), and finally to a phase-locked period-1 state ( ${\rm {P1}}_f$ ). The route to $2:1$ CDS is similar, but the quasiperiodic state hosts a doubled torus $(2\mathbb {T}^2_{2,f})$ that transforms into a phase-locked period-2 orbit $({\rm {P2}}_f)$ when CDS occurs. En route to PSC, the system transitions to a forced chaotic state ( ${\rm {CH}}_{1,2,f}$ ) followed by a phase-locked chaotic state, where $f_1$ , $f_2$ and $f_f$ still coexist but their phase difference remains bounded. We find that the maximum reduction in thermoacoustic amplitude occurs near the onset of CDS, and that the critical $\epsilon _f$ required for the onset of CDS does not vary significantly with $f_f$ . We then use two unidirectionally coupled Anishchenko–Astakhov oscillators to phenomenologically model the experimental synchronization dynamics, including (i) the route to $1:1$ CDS, (ii) various phase dynamics, such as phase drifting, slipping and locking, and (iii) the thermoacoustic amplitude variations in the $f_f/f_1$ – $\epsilon _f$ plane. This study extends the applicability of open-loop control further to a chaotic thermoacoustic system, demonstrating (i) the feasibility of using an existing actuation strategy to weaken aperiodic thermoacoustic oscillations, and (ii) the possibility of developing new active suppression strategies based on both established and emerging methods of chaos control.

Synchronization in network motifs of three piecewise Rössler systems coupled in ring configuration

In this work, we study the synchronization in the network motifs of three piecewise Rössler systems that exhibit coexistence of two attractors, coupled in ring configuration, in particular a bidirectional auxiliary coupling. For this configuration, we analyze the interaction of the systems by varying the coupling strengths, in order to characterize the conditions under which complete synchronization between the three systems can be achieved. The numerical results prove that the interaction of various multistable chaotic systems causes different types of synchronization and very complex dynamics between the systems is achieved. We obtain complete synchronization between the three systems and find the range of values of the coupling strengths where the distinct types of synchronization occur.

Fixed-time synchronization of multiplex networks by sliding mode control

Multiplex networks involve different types of synchronization due to their complex spatial structure. How to control multiplex networks to achieve different types of synchronization is an interesting topic. This paper considers the fixed-time synchronization of multiplex networks under sliding mode control (SMC). Firstly, for realizing three types of synchronization of multiplex networks in a fixed time, a unified sliding mode surface (SMS) is established. After that, based on the theory of SMC, a sliding mode controller (SMCr) which is more intelligent and has a simpler form than those in the existing literature is put forward for multiplex networks. It can not only guarantee the emergence of sliding mode motion, but also can realize three different kinds of synchronization by adjusting some parameters or even one parameter of the controller. Based on some theories of fixed-time stability, this paper deduces several sufficient conditions for the trajectories of the system to reach the preset SMS in a fixed time, and derives some sufficient conditions for multiplex networks to realize three different types of fixed-time synchronization. At the same time, the settling time which can reveal what factors determine the fixed-time synchronization in multiplex networks is obtained. Finally, in numerical simulations, different chaotic systems are set for each layer of multiplex networks to represent the nodes of different layers, which can prove that the theoretical results are practical and effective.

Analytical studies on complete, lag and anticipation synchronization in cascaded circuits with numerical and experimental confirmation

We report in this paper, the explicit analytical solutions developed for studying the different types of synchronization behaviors such as complete, lag and anticipation synchronization observed in cascaded circuits without any delay factors in the system. The Pecora–Carroll method of synchronization of unidirectionally coupled systems, which has not been earlier studied through explicit analytical solutions is reported in this paper. The emergence of different synchronization phenomena and the nature of evolution of the synchronization behavior has been discussed. Further, it has also been confirmed that the evolution of anticipation from lag through complete synchronization along with the attenuation, amplification of the subsystem signal occurs as a generalized phenomenon irrespective of the nature of the chaotic attractor state of the drive and the system parameters. The Hamilton energy of the cascaded system for different types of synchronization is reported. The numerical simulation and electronic circuit experimental results are presented to confirm the analytical results.

Cycle dynamics and synchronization in a coupled network of peripheral circadian clocks.

The intercellular interactions between peripheral circadian clocks, located in tissues and organs other than the suprachiasmatic nuclei of the hypothalamus, are still very poorly understood. We propose a theoretical and computational study of the coupling between two or more clocks, using a calibrated, reduced model of the circadian clock to describe some synchronization properties between peripheral cellular clocks. Based on a piecewise linearization of the dynamics of the mutual CLOCK:BMAL1/PER:CRY inactivation term, we suggest a segmentation of the circadian cycle into six stages, to help analyse different types of synchronization between two clocks, including single stage duration, total period and maximal amplitudes. Finally, our model reproduces some recent experimental results on the effects of different regimes of time-restricted feeding in liver circadian clocks of mice.

Synchronization issue of coupled neural networks based on flexible impulse control

The global exponential synchronization issue of coupled neural networks with time-delayed impulses is investigated in this paper. On the basis of the characteristics of coupled neural networks and theorems, we have built a novel coupled systems model. In order to fit the real situation, the impulses are flexible and it can beyond the impulsive interval under certain conditions in this paper. Therefore, our results are less restrictive and more practical compared to existing research. Besides, by using average impulsive delay (AID) and average impulsive interval (AII), we investigate two different effects of impulses on synchronization respectively and get a few adequate conditions for different types of synchronization. Finally, there are two examples of numerical simulations presented to illustrate the efficiency of the conclusions.

Determining efficiency of small-world algorithms: A comparative approach

In this paper, a comparison between three small-world algorithms is performed. Fixed-size complex networks are used to investigate efficiency of small-world property promoting synchronization. Cooperative behavior is determined through its transition point to the synchronized state. The presence of different types of synchronization characterizes the efficiency of the algorithms. Non-linear systems that exhibit chaos are used to compose the complex networks.

Fundamental Concepts of Synchronization

Objects with rhythms naturally synchronize. Synchronization is the coordination of events in order to run the system uniformly. Yet the phenomenon went entirely undocumented until 1665. Since the pioneering description of synchronization by Huygens, the phenomenon has been studied by various researchers in an interdisciplinary manner. Many researchers have contributed to the development of synchronization theory proving that synchronization occurs in coupled non-linear dissipative oscillators. Such oscillators range from mechanical clocks and population dynamics to human heart and neural networks. This article aims to explain the basic principles of synchronization theory. The history and applications of synchronization are discussed in real-world scenarios. We address different types of synchronization with a detailed discussion on the simplest type of synchronization. The phenomenon of synchronization applies to oscillations of different forms—periodic, noisy, and chaotic in nature. Here, we specifically discuss the oscillators which can hold synchronization. In particular, we provide an overview of self-sustained periodic and chaotic oscillators with a detailed description of different forms of these oscillators in phase space. Further, a summary of further research challenges has also been given for the future development of advanced applications based on natural synchronization phenomenon.

Dynamics of coupled generators of quasiperiodic oscillations: Different types of synchronization and other phenomena

Abstract A problem of synchronization of quasiperiodic oscillations is discussed in application to an example of coupled systems with autonomous quasiperiodic dynamics. Charts of Lyapunov exponents are presented that reveal characteristic domains on the parameter plane such as oscillator death, complete synchronization, phase synchronization of quasiperiodic oscillations, broadband synchronization, broadband quasiperiodicity. Features of each kind of dynamical behavior are discussed. Analysis of corresponding bifurcations is presented, including quasiperiodic Hopf bifurcations, saddle–node bifurcations of invariant tori of different dimensions, and bifurcations of torus doublings. Both the case of dominance of quasiperiodic oscillations in one of the generators and the case of pronounced periodic resonances embedded in the region of quasiperiodicity are considered.

Exponential lag function projective synchronization of memristor-based multidirectional associative memory neural networks via hybrid control

This paper is concerned with the exponential lag function projective synchronization of memristive multidirectional associative memory neural networks (MMAMNNs). First, we propose a new model of MMAMNNs with mixed time-varying delays. In the proposed approach, the mixed delays include time-varying discrete delays and distributed time delays. Second, we design two kinds of hybrid controllers. Traditional control methods lack the capability of reflecting variable synaptic weights. In this paper, the controllers are carefully designed to confirm the process of different types of synchronization in the MMAMNNs. Third, sufficient criteria guaranteeing the synchronization of system are derived based on the derive-response concept. Finally, the effectiveness of the proposed mechanism is validated with numerical experiments.

Strong generalized synchronization with a particular relationship R between the coupled systems

The question of the chaotic synchronization of two coupled dynamical systems is an issue that interests researchers in many fields, from biology to psychology, through economics, chemistry, physics, and many others. The different forms of couplings and the different types of synchronization, give rise to many problems, most of them little studied. In this paper we deal with general couplings of two dynamical systems and we study strong generalized synchronization with a particular relationship R between them. Our results include the definition of a window in the domain of the coupling strength, where there is an exponentially stable solution, and the explicit determination of this window. In the case of unidirectional or symmetric couplings, this window is presented in terms of the maximum Lyapunov exponent of the systems. Examples of applications to chaotic systems of dimension one and two are presented.

A study of synchronization processes of nonlinear systems in the difference space of phase variables

The analysis of trajectories in the phase space of the systems of ordinary differential equations has been made. Classification of phase trajectories has been developed. Synchronization in Rossler systems, coupled by the scheme “main–controlled” system, has been studied. In the controlled system, variables in the right –hand side are replaced by functions of time, which are solutions to the main system. The analysis of processes in nonlinear systems was made by means of replacement with the help of synchronization matrix and transfer to the linearized system of variables equal to the difference of phase variables of the main and controlled systems. As a result of this analysis, there have been set the values of the synchronization matrix elements in which there occur different types of synchronization: complete, phase and topological. It is shown that even in the absence of communication between Rossler systems in the difference space of phase variables of the main and controlled systems with nonlinear dynamics, there occurs topological synchronization and there is formed an attractor with low spatial complexity that is an open trajectory of limited values. The criterion for the absence of synchronization of nonlinear systems is the unlimited growth of the difference of phase variables

Different types of synchronization in coupled network based chaotic circuits

We propose a simple and new unified method to achieve lag, complete and anticipatory synchronizations in coupled nonlinear systems. It can be considered as an alternative to the subsystem and intentional parameter mismatch methods. This novel method is illustrated in a unidirectionally coupled RC phase shift network based Chua’s circuit. Employing feedback coupling, different types of chaos synchronization are observed experimentally and numerically in coupled identical chaotic oscillators without using time delay. With a simple switch in the experimental set up we observe different kinds of synchronization. We also analyze the coupled system with numerical simulations.

Effects of Spike Anticipation on the Spiking Dynamics of Neural Networks.

Synchronization is one of the central phenomena involved in information processing in living systems. It is known that the nervous system requires the coordinated activity of both local and distant neural populations. Such an interplay allows to merge different information modalities in a whole processing supporting high-level mental skills as understanding, memory, abstraction, etc. Though, the biological processes underlying synchronization in the brain are not fully understood there have been reported a variety of mechanisms supporting different types of synchronization both at theoretical and experimental level. One of the more intriguing of these phenomena is the anticipating synchronization, which has been recently reported in a pair of unidirectionally coupled artificial neurons under simple conditions (Pyragiene and Pyragas, 2013), where the slave neuron is able to anticipate in time the behavior of the master one. In this paper, we explore the effect of spike anticipation over the information processing performed by a neural network at functional and structural level. We show that the introduction of intermediary neurons in the network enhances spike anticipation and analyse how these variations in spike anticipation can significantly change the firing regime of the neural network according to its functional and structural properties. In addition we show that the interspike interval (ISI), one of the main features of the neural response associated with the information coding, can be closely related to spike anticipation by each spike, and how synaptic plasticity can be modulated through that relationship. This study has been performed through numerical simulation of a coupled system of Hindmarsh–Rose neurons.

Generalized Function Projective Combination-Combination Synchronization of Chaos in Third Order Chaotic Systems

In this paper, a generalized function projective combination-combination synchronization scheme (GFPCCS) among four chaotic systems is investigated via the active backstepping technique. To validate the proposed GFPCCS, suitable controllers are designed via the active backstepping technique to achieve GFPCCS among four chaotic Josephson junctions evolving from different initial conditions. The numerical simulations carried out show the achievement and effectiveness of the GFPCCS for the four chaotic Josephson junctions via the active backstepping technique. The results show that different types of synchronization can be achieved from the GFPCCS based on the choice of the scaling parameters, hence the GFPCCS could be used to modify the behaviour of coupled systems.

Synchronization of Slowly Rotating Nonidentically Driven Pendula

We study the synchronization of two rotating pendula mounted on a horizontal beam, which can roll on the parallel surface. The pendula are forced to rotate by different driving torques. It has been shown that after a transient two different types of synchronization between the pendula can be observed. The approximate analytical methods allow us to derive the synchronization conditions and explain the observed types of synchronous configurations. The energy balance in the system allows us to show how the energy is transferred between the pendula via the oscillating beam.

New type of synchronization of oscillators with hard excitation

It is shown that stable limiting cycles corresponding to nonlinear beats with complete energy exchange between oscillators can exist in a system of two weakly coupled active oscillators (generators). The oscillatory regime of this type, which implements a new type of synchronization in an active system, is an alternative to the well-studied synchronization in a regime close to a nonlinear normal mode. In this case, the ranges of dissipative parameters corresponding to different types of synchronization do not intersect. The analytic description of attractors revealed in analysis is based on the concept of limiting phase trajectories, which was developed earlier by one of the authors for conservative systems. A transition (in the parametric space) from the complete energy exchange between oscillators to predominant localization of energy in one of the oscillators can be naturally described using this concept. The localized normal mode is an attractor in the range of parameters in which neither the limiting phase trajectory nor any of the collective normal modes is an attractor.

Exact synchronization bound for coupled time-delay systems

We obtain an exact bound for synchronization in coupled time-delay systems using the generalized Halanay inequality for the general case of time-dependent delay, coupling, and coefficients. Furthermore, we show that the same analysis is applicable to both uni- and bidirectionally coupled time-delay systems with an appropriate evolution equation for their synchronization manifold, which can also be defined for different types of synchronization. The exact synchronization bound assures an exponential stabilization of the synchronization manifold which is crucial for applications. The analytical synchronization bound is independent of the nature of the modulation and can be applied to any time-delay system satisfying a Lipschitz condition. The analytical results are corroborated numerically using the Ikeda system.

Synchronization in Vehicle Routing—A Survey of VRPs with Multiple Synchronization Constraints

This paper presents a survey of vehicle routing problems with multiple synchronization constraints. These problems exhibit, in addition to the usual task covering constraints, further synchronization requirements between the vehicles, concerning spatial, temporal, and load aspects. They constitute an emerging field in vehicle routing research and are becoming a “hot” topic. The contribution of the paper is threefold: (i) It presents a classification of different types of synchronization. (ii) It discusses the central issues related to the exact and heuristic solution of such problems. (iii) It comprehensively reviews pertinent literature with respect to applications as well as successful solution approaches, and it identifies promising algorithmic avenues.

Synchronization transitions in coupled time-delay electronic circuits with a threshold nonlinearity

Experimental observations of typical kinds of synchronization transitions are reported in unidirectionally coupled time-delay electronic circuits with a threshold nonlinearity and two time delays, namely feedback delay τ(1) and coupling delay τ(2). We have observed transitions from anticipatory to lag via complete synchronization and their inverse counterparts with excitatory and inhibitory couplings, respectively, as a function of the coupling delay τ(2). The anticipating and lag times depend on the difference between the feedback and the coupling delays. A single stability condition for all the different types of synchronization is found to be valid as the stability condition is independent of both the delays. Further, the existence of different kinds of synchronizations observed experimentally is corroborated by numerical simulations and from the changes in the Lyapunov exponents of the coupled time-delay systems.