Experimental studies can provide powerful insights into the physics of complex networks. Here, we report experimental results on the influence of connection topology on synchronization in fiber-optic networks of chaotic optoelectronic oscillators. We find that the recently predicted nonmonotonic, cusplike synchronization landscape manifests itself in the rate of convergence to the synchronous state. We also observe that networks with the same number of nodes, same number of links, and identical eigenvalues of the coupling matrix can exhibit fundamentally different approaches to synchronization. This previously unnoticed difference is determined by the degeneracy of associated eigenvectors in the presence of noise and mismatches encountered in real-world conditions.

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 electro-optic 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 Lyapunov exponents or transverse Lyapunov exponents of the system, and we present an experimental method to determine these rates that does not require a mathematical model of the system. Finally, we demonstrate a new adaptive control method that keeps two oscillators synchronized, even when the coupling between them is changing unpredictably.

We experimentally observe the nonlinear dynamics of an optoelectronic time-delayed feedback loop designed for chaotic communication using commercial fiber optic links, and we simulate the system using delay differential equations. We show that synchronization of a numerical model to experimental measurements provides a new way to assimilate data and forecast the future of this time-delayed high-dimensional system. For this system, which has a feedback time delay of 22 ns, we show that one can predict the time series for up to several delay periods, when the dynamics is about 15 dimensional. The question of how to predict the future of a dynamical system with time delay is of interest in many applications [1][2]. In chaotic encrypted communication systems, the predictability is related to how difficult it would be for an eavesdropper to intercept a message. A better understanding of predictability in these systems could guide the development of new strategies to improve security, such as periodically changing the system parameters or protocols to avoid interception [3]. Prediction and anticipation are thought to underlie the process of image recognition and motion tracking in the retina [4]. In networked sensor arrays designed to detect spatiotemporal disturbances, prediction methods could enable efficient acquisition and incorporation of data from multiple sensors [5]. In biomedical treatment, prediction models could lead to improved strategies for adjusting drug dosage and delivery or physiological control [6].Recent studies on prediction address system identification and model development [7], as well as the use of anticipated synchronization between coupled identical systems [8]. In this work, we demonstrate that synchronization of a numerical model to an experimentally measured waveform allows us to both forecast the future dynamics of a high-dimensional system and estimate the local maximum Lyapunov exponent and its distribution. The inverse of the maximum Lyapunov exponent defines the prediction horizon -the time over which the system behavior can be forecast.The optoelectronic system studied is shown in Figure 1. A similar system was used by Argyris et al. as a transmitter and receiver for a high-speed chaotic communication 1

We experimentally demonstrate and numerically simulate an adaptive method to maintain synchronization between coupled nonlinear chaotic oscillators, when the coupling between the systems is unknown and time-varying (e.g., due to environmental parameter drift). The technique is applied to optoelectronic feedback loops exhibiting high-dimensional chaotic dynamics. In addition to keeping the two systems isochronally synchronized in the presence of a priori unknown time-varying coupling strength, the technique provides an estimate of the time-varying coupling.

We present and experimentally demonstrate a technique for achieving and maintaining a global state of identical synchrony of an arbitrary network of chaotic oscillators even when the coupling strengths are unknown and time-varying. At each node an adaptive synchronization algorithm dynamically estimates the current strength of the net coupling signal to that node. We experimentally demonstrate this scheme in a network of three bidirectionally coupled chaotic optoelectronic feedback loops and we present numerical simulations showing its application in larger networks. The stability of the synchronous state for arbitrary coupling topologies is analyzed via a master stability function approach.