Strong and weak chaos in networks of semiconductor lasers with time-delayed couplings

Nonlinear networks with time-delayed couplings may show strong and weak chaos, depending on the scaling of their Lyapunov exponent with the delay time. We study strong and weak chaos for semiconductor lasers, either with time-delayed self-feedback or for small networks. We examine the dependence on the pump current and consider the question of whether strong and weak chaos can be identified from the shape of the intensity trace, the autocorrelations, and the external cavity modes. The concept of the sub-Lyapunov exponent λ0 is generalized to the case of two time-scale-separated delays in the system. We give experimental evidence of strong and weak chaos in a network of lasers, which supports the sequence of weak to strong to weak chaos upon monotonically increasing the coupling strength. Finally, we discuss strong and weak chaos for networks with several distinct sub-Lyapunov exponents and comment on the dependence of the sub-Lyapunov exponent on the number of a laser's inputs in a network

Understanding the enhanced synchronization of delay-coupled networks with fluctuating topology

We study the dynamics of networks with coupling delay, from which the connectivity changes over time. The synchronization properties are shown to depend on the interplay of three time scales: the internal time scale of the dynamics, the coupling delay along the network links and time scale at which the topology changes. Concentrating on a linearized model, we develop an analytical theory for the stability of a synchronized solution. In two limit cases the system can be reduced to an “effective” topology: In the fast switching approximation, when the network fluctuations are much faster than the internal time scale and the coupling delay, the effective network topology is the arithmetic mean over the different topologies. In the slow network limit, when the network fluctuation time scale is equal to the coupling delay, the effective adjacency matrix is the geometric mean over the adjacency matrices of the different topologies. In the intermediate regime the system shows a sensitive dependence on the ratio of time scales, and specific topologies, reproduced as well by numerical simulations. Our results are shown to describe the synchronization properties of fluctuating networks of delay-coupled chaotic maps

Reservoir Computing Using Autonomous Boolean Networks Realized on Field-Programmable Gate Arrays

In this chapter, we consider realizing a reservoir computer on an electronic chip that allows for many tens of network nodes whose connection topology can be quickly reconfigured. The reservoir computer displays analog-like behavior and has the potential to perform computations beyond that of a classic Turning machine. In detail, we present our preliminary results of using a physical reservoir computer for performing the task of identifying written digits. The reservoir is realized on a commercially available electronic device known as a field-programmable gate array on which we create an autonomous Boolean network for information processing. Even though the network nodes are Boolean logic elements, they display analog behavior because there is no master clock that controls the nodes. In addition, the electronic signals related to the written-digit images are injected into the reservoir at high speed, leading to the possibility of full-image classification on the nanosecond time scale. We explore the dynamics of the autonomous Boolean networks in response to injected signals and, based on these results, investigate the performance of the reservoir computer on the written-digit task. For a wide range of reservoir structures, we obtain a typical performance of ∼ 90% for correctly identifying a written digit, which exceeds that obtained by a linear classifier. This work paves the way for achieving low-power, high-speed reservoir computing on readily available field-programmable gate arrays, which are well matched to existing computing infrastructure.DFG, 163436311, SFB 910: Kontrolle selbstorganisierender nichtlinearer Systeme: Theoretische Methoden und AnwendungskonzepteEC/H2020/713694/EU/International Mobility and Training in Photonics Programme/MULTIPL