Acoustic measurements of the infinitesimal phase response curve from a sounding organ pipe

The infinitesimal phase response curve (iPRC) of an organ pipe was measured using two types of external forcing, namely, sinusoidal and pulse forcing. Although the measured iPRCs exhibited different shapes because of the difficulty in realizing ideal pulses in acoustic experiments, the spectral structures agreed between both methods. Both measurements indicated that an external sound, which matched the pipe's second resonance, could most effectively induce frequency locking. Acoustically, this may be considered as a consequence of the pipe's open end. Our study is of significant importance in understanding the characteristics of frequency locking among organ pipes.     

Spectral coarse graining of complex clustered networks

Synchronization in complex dynamical networks is in the focus of network science today, where intensive efforts have been devoted to understanding its mechanisms and developing basic theories with applications. However, the sheer sizes of large-scale networks have been the main hurdle in such analysis and applications. Recently, a coarse graining scheme based on network synchronization was proposed to reduce the network size while preserving the synchronizability of the original network. In this research, we investigate the effects of the coarse graining process on synchronizability over complex clustered networks. Numerous experiments demonstrate a close correlation between the degree of clustering of the initial network and the ability of spectral coarse graining in preserving the network synchronizability. It is found that synchronizability can be well preserved after applying the spectral coarse graining if the considered network has a clear cluster structure, whereas this is not so for networks with vague clustering. Since most real-world networks have prominent cluster structures, this research provides new insights into understanding large-scale dynamical networks and analyzing their complex topological characteristics as well as synchronization mechanisms.     

A chaos secure communication scheme based on multiplication modulation

A secure spread spectrum communication scheme using multiplication modulation is proposed. The proposed system multiplies the message by chaotic signal. The scheme does not need to know the initial condition of the chaotic signals and the receiver is based on an extended Kalman filter (EKF). This signal encryption scheme lends itself to cheap implementation and can therefore be used effectively for ensuring security and privacy in commercial consumer electronics products. To illustrate the effectiveness of the proposed scheme, a numerical example based on Genesio-Tesi system and also Chen dynamical system is presented and the results are compared.     

Parameter estimation of delay dynamical system from a scalar time series under external noise

We introduce an adaptive learning rules for estimating all unknown parameters of delay dynamical system using a scalar time series. Sufficient condition for synchronization is derived using Krasovskii-Lyapunov theory. This scheme is highly applicable in secure communication since multiple messages can be transmitted through multiple parameter modulations. One of the advantage of this method is that parameter estimation is also possible even when only one time series of the transmitter is available. We present numerical examples for Mackey-Glass system with periodic delay time which are used to illustrate the validity of this scheme. The corresponding numerical results and the effect of external noise are also studied.     

Generalized Edwards Transformation and Principle of Permutation Invariance

The relativity of simultaneity is generalized by using the concept of synchronization gauge. The Lorentz transformation is derived without the postulate of the universal limiting speed, and a generalized Edwards transformation is obtained by using the principle of permutation invariance (covariance). It is shown that the existences of the one-way universal limiting speed (in the Lorentz transformation) and the constancy of the two-way average speed of light (in the Edwards transformation) are the necessary consequences of the principle of permutation invariance that is consistent with the postulate of relativity. The connection between the Edward transformation and the general coordinate transformation is discussed, and based on this, we find that the physical meaning of the Edwards parameter, which indicates anisotropy of the speed of light, is a gravitomagnetic potential of the spacetime.     

Complexity and synchronization in chaotic fiber-optic systems

In this work we investigate experimentally the complexity of chaotic attractors generated by a semiconductor laser subjected to optical feedback and associate their dimensionality with the synchronization efficiency of the corresponding chaotic transmitter-receiver configuration. The complexity is characterized by calculating the correlation dimension D₂ of experimental chaotic time series for different values of the optical feedback η. We present the effect of D₂ on the synchronization efficiency and determine the optimal operating condition that leads to the most complex chaotic carrier and, simultaneously, to the most successful synchronization. Lastly, we associate and explain our experimental results with theoretical predictions in the research literature.     

Properties of synchronization in the systems of non-identical coupled van der Pol and van der Pol-Duffing oscillators. Broadband synchronization

The particular properties of dynamics are discussed for dissipatively coupled van der Pol oscillators, non-identical in values of parameters controlling the Hopf bifurcation. Possibility of a special synchronization regime in an infinitively long band between oscillator death and quasiperiodic areas is shown for such system. Features of the bifurcation picture are discussed for different values of the control parameters and for the case of additional Duffing-type nonlinearity. Analysis of the slow-flow equations is presented.     

Design of PD controller for master-slave synchronization of Lur’e systems with time-delay

In this paper, design of PD controller for master-slave synchronization of Lur’e systems with time-delay has been considered. A new delay-dependent synchronization criterion is derived based on the integral inequality method and free weighting matrices. The criteria are given in terms of LMIs, which can be easily solved by LMI Toolbox in Matlab. A numerical example is given to illustrate the effectiveness of the method.     

Synchronization and functional central limit theorems for interacting reinforced random walks

We obtain Central Limit Theorems in Functional form for a class of time-inhomogeneous interacting random walks. Due to a reinforcement mechanism and interaction, the walks are strongly correlated and converge almost surely to the same, possibly random, limit. We study random walks interacting through a mean-field rule and compare the rate they converge to their limit with the rate of synchronization, i.e. the rate at which their mutual distances converge to zero. We show that, under certain conditions, synchronization is faster than convergence. Even if our focus is on theoretical results, we propose as main motivations two contexts in which such results could directly apply: urn models and opinion dynamics in a random network evolving via preferential attachment.     

Synchronization in complex networks with switching topology

This Letter investigates synchronization issues of complex dynamical networks with switching topology. By constructing a common Lyapunov function, we show that local and global synchronization for a linearly coupled network with switching topology can be evaluated by the time average of second smallest eigenvalues corresponding to the Laplacians of switching topology. This result is quite powerful and can be further used to explore various switching cases for complex dynamical networks. Numerical simulations illustrate the effectiveness of the obtained results in the end.