Using synchronism of chaos for adaptive learning of network topology

In this paper we consider networks of dynamical systems that evolve in synchrony and investigate how dynamical information from the synchronization dynamics can be effectively used to learn the network topology, i.e., identify the time evolution of the couplings between the network nodes. To this aim, we present an adaptive strategy that, based on a potential that the network systems seek to minimize in order to maintain synchronization, can be successfully applied to identify the time evolution of the network from limited information. This strategy takes advantage of the properties of synchronism of chaos and of the presence of different communication delays over the network links. As a motivating example we consider a network of sensors surveying an area, in which information regarding the time evolution of the network connections can be used, e.g., to detect changes taking place within the area. We propose two different setups for our strategy. In the first one, synchronization has to be achieved at each node (as well as the identification of the couplings over the network links), based solely on a single scalar signal representing a superposition of signals from the other nodes in the network. In the second one, we incorporate an additional node, termed the maestro, having the function of maintaining network synchronization. We will see that when such an arrangement is realized, it will become possible to effectively identify the time evolution of networks that are much larger than would be possible in the absence of a maestro.Comment: 22 pages, 12 figures, accepted for publication on Physical Review

Performance Analysis of Physical Layer Network Coding for Two-way Relaying over Non-regenerative Communication Satellites

Two-way relaying is one of the major applications of broadband communication satellites, for which an efficient technique is Physical Layer Network Coding (PLNC). Earlier studies have considered satellites employing PLNC with onboard processing. This paper investigates the performance of PLNC over non-regenerative satellites, as a majority of the operational and planned satellites have no onboard processing. Assuming that the channel magnitudes of the two users are equal, two operating conditions are considered with uncoded-QPSK relaying. In the first condition, both users are completely synchronized in phase and transmit power, and in the second condition, phase is not synchronized. The peak power constraint imposed by the satellite amplifier is considered and the error performance bounds are derived for both the conditions. The simulation results for end-to-end Bit Error Rate (BER) and throughput are provided. These results shall enable communication system designers to decide system parameters like power and linearity, and perform tradeoff analysis between different relaying schemes.Comment: 9 pages and 13 figure

The stability of adaptive synchronization of chaotic systems

In past works, various schemes for adaptive synchronization of chaotic systems have been proposed. The stability of such schemes is central to their utilization. As an example addressing this issue, we consider a recently proposed adaptive scheme for maintaining the synchronized state of identical coupled chaotic systems in the presence of a priori unknown slow temporal drift in the couplings. For this illustrative example, we develop an extension of the master stability function technique to study synchronization stability with adaptive coupling. Using this formulation, we examine local stability of synchronization for typical chaotic orbits and for unstable periodic orbits within the synchronized chaotic attractor (bubbling). Numerical experiments illustrating the results are presented. We observe that the stable range of synchronism can be sensitively dependent on the adaption parameters, and we discuss the strong implication of bubbling for practically achievable adaptive synchronization.Comment: 21 pages, 6 figure

Physics and Applications of Laser Diode Chaos

An overview of chaos in laser diodes is provided which surveys experimental achievements in the area and explains the theory behind the phenomenon. The fundamental physics underpinning this behaviour and also the opportunities for harnessing laser diode chaos for potential applications are discussed. The availability and ease of operation of laser diodes, in a wide range of configurations, make them a convenient test-bed for exploring basic aspects of nonlinear and chaotic dynamics. It also makes them attractive for practical tasks, such as chaos-based secure communications and random number generation. Avenues for future research and development of chaotic laser diodes are also identified.Comment: Published in Nature Photonic

Connectivity Influences on Nonlinear Dynamics in Weakly-Synchronized Networks: Insights from Rössler Systems, Electronic Chaotic Oscillators, Model and Biological Neurons

Natural and engineered networks, such as interconnected neurons, ecological and social networks, coupled oscillators, wireless terminals and power loads, are characterized by an appreciable heterogeneity in the local connectivity around each node. For instance, in both elementary structures such as stars and complex graphs having scale-free topology, a minority of elements are linked to the rest of the network disproportionately strongly. While the effect of the arrangement of structural connections on the emergent synchronization pattern has been studied extensively, considerably less is known about its influence on the temporal dynamics unfolding within each node. Here, we present a comprehensive investigation across diverse simulated and experimental systems, encompassing star and complex networks of Rössler systems, coupled hysteresis-based electronic oscillators, microcircuits of leaky integrate-and-fire model neurons, and finally recordings from in-vitro cultures of spontaneously-growing neuronal networks. We systematically consider a range of dynamical measures, including the correlation dimension, nonlinear prediction error, permutation entropy, and other information-theoretical indices. The empirical evidence gathered reveals that under situations of weak synchronization, wherein rather than a collective behavior one observes significantly differentiated dynamics, denser connectivity tends to locally promote the emergence of stronger signatures of nonlinear dynamics. In deterministic systems, transition to chaos and generation of higher-dimensional signals were observed; however, when the coupling is stronger, this relationship may be lost or even inverted. In systems with a strong stochastic component, the generation of more temporally-organized activity could be induced. These observations have many potential implications across diverse fields of basic and applied science, for example, in the design of distributed sensing systems based on wireless coupled oscillators, in network identification and control, as well as in the interpretation of neuroscientific and other dynamical data

Synchronization and prediction of chaotic dynamics on networks of optoelectronic oscillators

The subject of this thesis is the exploration of chaotic synchronization for novel applications including time-series prediction and sensing. We begin by characterizing the nonlinear dynamics of an optoelectronic time-delayed feedback loop. We show that synchronization of an accurate numerical model to experimental measurements provides a way to assimilate data and forecast the future of deterministic chaotic behavior. Next, we implement an adaptive control method that maintains isochronal synchrony for a network of coupled feedback loops when the interaction strengths are unknown and time-varying. Control signals are used as real-time estimates of the variations present within the coupling paths. We analyze the stability of synchronous solutions for arbitrary coupling topologies via a modified master stability function that incorporates the adaptation response dynamics. Finally, we show that the master stability function, which is derived from a set of linearized equations, can also be experimentally measured using a two-node network, and it can be applied to predict the convergence behavior of large networks

Breathing synchronization in interconnected networks

Global synchronization in a complex network of oscillators emerges from the interplay between its topology and the dynamics of the pairwise interactions among its numerous components. When oscillators are spatially separated, however, a time delay appears in the interaction which might obstruct synchronization. Here we study the synchronization properties of interconnected networks of oscillators with a time delay between networks and analyze the dynamics as a function of the couplings and communication lag. We discover a new breathing synchronization regime, where two groups appear in each network synchronized at different frequencies. Each group has a counterpart in the opposite network, one group is in phase and the other in anti-phase with their counterpart. For strong couplings, instead, networks are internally synchronized but a phase shift between them might occur. The implications of our findings on several socio-technical and biological systems are discussed.Comment: 7 pages, 3 figures + 3 pages of Supplemental Materia