Due to time delays in signal transmission and processing, phase lags are inevitable in realistic complex oscillator networks. Conventional wisdom is that phase lags are detrimental to network synchronization. Here we show that judiciously chosen phase lag modulations can result in significantly enhanced network synchronization. We justify our strategy of phase modulation, demonstrate its power in facilitating and enhancing network synchronization with synthetic and empirical network models, and provide an analytic understanding of the underlying mechanism. Our work provides a new approach to synchronization optimization in complex networks, with insights into control of complex nonlinear networks.
We report enhancing of complete synchronization in identical chaotic oscillators when their interaction is mediated by a mismatched oscillator. The identical oscillators now interact indirectly through the intermediate relay oscillator. The induced heterogeneity in the intermediate oscillator plays a constructive role in reducing the critical coupling for a transition to complete synchronization. A common lag synchronization emerges between the mismatched relay oscillator and its neighboring identical oscillators that leads to this enhancing effect. We present examples of one-dimensional open …
We investigate synchronization in the presence of delay time modulation for application to communication. We have observed that the robust synchronization is established by a common delay signal and its threshold is presented using Lyapunov exponents analysis. The influence of the delay time modulation in chaotic oscillators is also discussed.
Existence of a new type of oscillating synchronization that oscillates between three different types of synchronizations (anticipatory, complete and lag synchronizations) is identified in unidirectionally coupled nonlinear time-delay systems having two different time-delays, that is feedback delay with a periodic delay time modulation and a constant coupling delay. Intermittent anticipatory, intermittent lag and complete synchronizations are shown to exist in the same system with identical delay time modulations in both the delays. The transition from anticipatory to complete synchronization a…
We have found a synchronization behavior between two identical chaotic systems^M when their delay times are modulated by a common irregular signal. ^M This phenomenon is demonstrated both in two identical chaotic maps whose delay times are driven by a common^M chaotic or random signal and in two identical chaotic oscillators whose delay times are driven by^M a signal of another chaotic oscillator. We analyze the phenomenon by using^M the Lyapunov exponents and discuss it in relation with generalized synchronization.^M
We study the synchronization and stability of power grids within the Kuramoto phase oscillator model with inertia with a bimodal frequency distribution representing the generators and the loads. We identify critical nodes through solitary frequency deviations and Lyapunov vectors corresponding to unstable Lyapunov exponents. To cure dangerous deviations from synchronization we propose time-delayed feedback control, which is an efficient control concept in nonlinear dynamic systems. Different control strategies are tested and compared with respect to the minimum number of controlled nodes requi…
By a model of coupled phase oscillators, we show analytically how synchronization in {\em non-identical} complex networks can be enhanced by introducing a proper gradient into the couplings. It is found that, by pointing the gradient from the large-degree to the small-degree nodes on each link, increasing the gradient strength will bring forward the {\em onset} of network synchronization monotonically, and, under the same gradient strength, heterogeneous networks are more synchronizable than homogeneous networks. These findings are verified by extensive simulations.
Synchronization processes in populations of identical networked oscillators are in the focus of intense studies in physical, biological, technological and social systems. Here we analyze the stability of the synchronization of a network of oscillators coupled through different variables. Under the assumption of an equal topology of connections for all variables, the master stability function formalism allows assessing and quantifying the stability properties of the synchronization manifold when the coupling is transferred from one variable to another. We report on the existence of an optimal c…
Heterogeneity in the degree (connectivity) distribution has been shown to suppress synchronization in networks of symmetrically coupled oscillators with uniform coupling strength (unweighted coupling). Here we uncover a condition for enhanced synchronization in directed networks with weighted coupling. We show that, in the optimum regime, synchronizability is solely determined by the average degree and does not depend on the system size and the details of the degree distribution. In scale-free networks, where the average degree may increase with heterogeneity, synchronizability is drastically …
In this paper, we report a novel approach for studying the effect of optimal uncoupling on the stability of synchronization in coupled chaotic systems. The clipping of phase space of the driven system having an orientation along the coordinate axes revealing the nature of coupling of the state variables of coupled systems is identified in certain coupled third-order chaotic systems. The stability of synchronization is studied through the {\emph{Master Stability Function}} (MSF). The optimal directions of implementing the clipping width to achieve stable synchronization is observed by studying …
Nonlinear dynamical systems possessing an invariant subspace in the phase space and chaotic or stochastic motion within the subspace often display on-off intermittency close to the threshold of stability of the subspace. In a class of symmetric systems, the intermittency is symmetry-breaking [Ying-Cheng Lai, Phys. Rev. E {\bf 53}. R4267 (1996)]. We report interesting and practically important universal behavior of robustness of supersensitivity, resonance and information gain in this class of systems when subjected to a weak modulation. While intermittent loss of synchronization may be harmful…
In a large variety of systems (biological, physical, social etc.), synchronization occurs when different oscillating objects tune their rhythm when they interact with each other. The different underlying network defining the connectivity properties among these objects drives the global dynamics in a complex fashion and affects the global degree of synchrony of the system. Here we study the impact of such types of different network architectures, such as Fully-Connected, Random, Regular ring lattice graph, Small-World and Scale-Free in the global dynamical activity of a system of coupled Kuramo…
It has been proposed to realize secure communication using chaotic synchronization via transmission of binary message encoded by parameter modulation in the chaotic system. This paper considers the use of parameter adaptive control techniques to extract the message, based on the assumptions that we know the equation form of the chaotic system in the transmitter but do not have access to the precise values of the parameters which are kept secret as a secure set. In the case that a synchronizing system can be constructed using parameter adaptive control by the transmitted signal and the synchron…
The global structure of the Isochrons and the corresponding Phase Response Curves are, for the first time, investigated and numerically computed for the fundamental photonic oscillator consisted of an Optically Injected Laser. Their crucial role in the synchronization dynamics under a periodic modulation of the injection beam is shown, along with their capability for providing conditions for stable phase-locking and periodic outputs with discrete equidistant spectra in the form of frequency combs.
We study the effect of parameter fluctuations on synchronization of a coupled chaotic system. The fluctuations to the parameter can be random or it can be a periodic modulation. For random fluctuations we introduce a new quantity, the \emph{rate of fluctuations}, apart from the statistical features of the fluctuations. Fluctuation rate in our study refers to the number of random modifications to parameters occurring in unit time. With a periodic modulation, the fluctuation rates can be the frequency of the modulating term. It is found that with high fluctuation rates the synchronization is sta…
The dynamics of an oscillator driven by both low- and high- frequency external signals is studied. It is shown that both two- and three-frequency resonances arise due to a nonlinear interaction of these harmonic forces. Conditions which must be met for oscillator synchronization under these resonances are estimated analytically by considering the Van der Pol oscillator with modulated natural frequency as mathematical model. It is demonstrated that due to the low-frequency modulation, additional synchronization regions arise in the control parameter space. Feasibility of the theoretical finding…
We study the dynamics of phase synchronization in growing populations of discrete phase oscillatory systems when the division process is coupled to the distribution of oscillator phases. Using mean field theory, linear stability analysis, and numerical simulations, we demonstrate that coupling between population growth and synchrony can lead to a wide range of dynamical behavior, including extinction of synchronized oscillations, the emergence of asynchronous states with unequal state (phase) distributions, bistability between oscillatory and asynchronous states or between two asynchronous sta…
We study the synchronization of chaotic units connected through time-delayed fluctuating interactions. We focus on small-world networks of Bernoulli and Logistic units with a fixed chiral backbone. Comparing the synchronization properties of static and fluctuating networks, we find that random network alternations can enhance the synchronizability. Synchronized states appear to be maximally stable when fluctuations are much faster than the time-delay, even when the instantaneous state of the network does not allow synchronization. This enhancing effect disappears for very slow fluctuations. Fo…
We describe a flexible and modular delayed-feedback nonlinear oscillator that is capable of generating a wide range of dynamical behaviours, from periodic oscillations to high-dimensional chaos. The oscillator uses electrooptic modulation and fibre-optic transmission, with feedback and filtering implemented through real-time digital-signal processing. We consider two such oscillators that are coupled to one another, and we identify the conditions under which they will synchronize. By examining the rates of divergence or convergence between two coupled oscillators, we quantify the maximum Lyapu…
