Experiments with arbitrary networks in time-multiplexed delay systems

Abstract

We report a new experimental approach using an optoelectronic feedback loop to investigate the dynamics of oscillators coupled on large complex networks with arbitrary topology. Our implementation is based on a single optoelectronic feedback loop with time delays. We use the space-time interpretation of systems with time delay to create large networks of coupled maps. Others have performed similar experiments using high-pass filters to implement the coupling; this restricts the network topology to the coupling of only a few nearest neighbors. In our experiment, the time delays and coupling are implemented on a field-programmable gate array, allowing the creation of networks with arbitrary coupling topology. This system has many advantages: the network nodes are truly identical, the network is easily reconfigurable, and the network dynamics occur at high speeds. We use this system to study cluster synchronization and chimera states in both small and large networks of different topologies.

Symmetry- and input-cluster synchronization in networks

“…In Sec. IV we describe the stability of the orbital and equitable clusters and present an experimental verification of their stability using a network of optoelectronic oscillators [7].…”

A poor man’s coherent Ising machine based on opto-electronic feedback systems for solving optimization problems

“…In the Methods section, we show how this output approximates the coherent superposition of DOPO pulses in DOPO-based CIMs. By coupling the output of multiple OEOs together, either electrically or optically 22,23 , a network of bistable optical states can thus be generated to represent an ensemble of Ising spins. Contrary to DOPO-based CIMs however, generation, interference, and detection of the optical states is fully contained within the MZM and the feedback system.…”

Laminar chaos in experiments and nonlinear delayed Langevin equations: A time series analysis toolbox for the detection of laminar chaos

“…We now describe how we obtained this value for the noise strength. We use the exact same apparatus used for our observations of Laminar Chaos; however, we reconfigure the FPGA as described in [57], so that the system behaves as two coupled truly identical opto-electronic maps. This system can be modeled as = δ m,m .…”

“…III we explain the experimental realization of Laminar Chaos by an opto-electronic setup similar to the one in Ref. [57]. Results of the experiments are presented, where we demonstrate that Laminar Chaos is robust against experimental and measurement noise.…”