David P. Rosin

Transient scaling and resurgence of chimera states in networks of Boolean phase oscillators

We study networks of nonlocally coupled electronic oscillators that can be described approximately by a Kuramoto-like model. The experimental networks show long complex transients from random initial conditions on the route to network synchronization. The transients display complex behaviors, including resurgence of chimera states, which are network dynamics where order and disorder coexists. The spatial domain of the chimera state moves around the network and alternates with desynchronized dynamics. The fast time scale of our oscillators (on the order of 100ns) allows us to study the scaling of the transient time of large networks of more than a hundred nodes, which has not yet been confirmed previously in an experiment and could potentially be important in many natural networks. We find that the average transient time increases exponentially with the network size and can be modeled as a Poisson process in experiment and simulation. This exponential scaling is a result of a synchronization rate that follows a power law of the phase-space volume.

Control of synchronization patterns in neural-like Boolean networks.

We study experimentally the synchronization patterns in time-delayed directed Boolean networks of excitable systems. We observe a transition in the network dynamics when the refractory time of the individual systems is adjusted. When the refractory time is on the same order of magnitude as the mean link time delays or the heterogeneities of the link time delays, cluster synchronization patterns change, or are suppressed entirely, respectively. We also show that these transitions occur when we change the properties of only a small number of driver nodes identified by their larger in degree; hence, the synchronization patterns can be controlled locally by these nodes. Our findings have implications for synchronization in biological neural networks.

SYNCHRONIZATION OF COUPLED NEURAL OSCILLATORS WITH HETEROGENEOUS DELAYS

We investigate the effects of heterogeneous delays on the coupling of two excitable neural systems. Depending upon the coupling strengths and the time delays in the mutual and self-coupling systems, the compound system exhibits different types of synchronized oscillations of variable period. We analyze this synchronization based on the interplay of the different time delays and support the numerical results by analytical findings. In addition, we elaborate on bursting-like dynamics with two competing timescales on the basis of the autocorrelation function.

Pulse-train solutions and excitability in an optoelectronic oscillator

We study an optoelectronic time-delay oscillator with bandpass filtering for different values of the filter bandwidth. Our experiments show novel pulse-train solutions with pulse widths that can be controlled over a three-order-of-magnitude range, with a minimum pulse width of ∼ 150 ps. The equations governing the dynamics of our optoelectronic oscillator are similar to the FitzHugh-Nagumo model from neurodynamics with delayed feedback in the excitable and oscillatory regimes. Using a nullclines analysis, we derive an analytical proportionality between pulse width and the low-frequency cutoff of the bandpass filter, which is in agreement with experiments and numerical simulations. Furthermore, the nullclines help to describe the shape of the waveforms. Copyright c � EPLA, 2011

Reservoir computing with a single time-delay autonomous Boolean node

We demonstrate reservoir computing with a physical system using a single autonomous Boolean logic element with time-delay feedback. The system generates a chaotic transient with a window of consistency lasting between 30 and 300 ns, which we show is sufficient for reservoir computing. We then characterize the dependence of computational performance on system parameters to find the best operating point of the reservoir. When the best parameters are chosen, the reservoir is able to classify short input patterns with performance that decreases over time. In particular, we show that four distinct input patterns can be classified for 70 ns, even though the inputs are only provided to the reservoir for 7.5 ns.

Synchronization of coupled Boolean phase oscillators.

We design, characterize, and couple Boolean phase oscillators that include state-dependent feedback delay. The state-dependent delay allows us to realize an adjustable coupling strength, even though only Boolean signals are exchanged. Specifically, increasing the coupling strength via the range of state-dependent delay leads to larger locking ranges in uni- and bidirectional coupling of oscillators in both experiment and numerical simulation with a piecewise switching model. In the unidirectional coupling scheme, we unveil asymmetric triangular-shaped locking regions (Arnold tongues) that appear at multiples of the natural frequency of the oscillators. This extends observations of a single locking region reported in previous studies. In the bidirectional coupling scheme, we map out a symmetric locking region in the parameter space of frequency detuning and coupling strength. Because of the large scalability of our setup, our observations constitute a first step towards realizing large-scale networks of coupled oscillators to address fundamental questions on the dynamical properties of networks in a new experimental setting.

Experiments on autonomous Boolean networks

We realize autonomous Boolean networks by using logic gates in their autonomous mode of operation on a field-programmable gate array. This allows us to implement time-continuous systems with complex dynamical behaviors that can be conveniently interconnected into large-scale networks with flexible topologies that consist of time-delay links and a large number of nodes. We demonstrate how we realize networks with periodic, chaotic, and excitable dynamics and study their properties. Field-programmable gate arrays define a new experimental paradigm that holds great potential to test a large body of theoretical results on the dynamics of complex networks, which has been beyond reach of traditional experimental approaches.

Ultrafast physical generation of random numbers using hybrid Boolean networks

We describe a high-speed physical random number generator based on a hybrid Boolean network with autonomous and clocked logic gates, realized on a reconfigurable chip. The autonomous logic gates are arranged in a bidirectional ring topology and generate broadband chaos. The clocked logic gates receive input from the autonomous logic gates so that random numbers are generated physically that pass standard randomness tests without further postprocessing. The large number of logic gates on reconfigurable chips allows for parallel generation of random numbers, as demonstrated by our implementation of 128 physical random number generators that achieve a real-time bit rate of 12.8Gbits/s.

Multirhythmicity in an optoelectronic oscillator with large delay

An optoelectronic oscillator exhibiting a large delay in its feedback loop is studied both experimentally and theoretically. We show that multiple square-wave oscillations may coexist for the same values of the parameters (multirhythmicity). Depending on the sign of the phase shift, these regimes admit either periods close to an integer fraction of the delay or periods close to an odd integer fraction of twice the delay. These periodic solutions emerge from successive Hopf bifurcation points and stabilize at a finite amplitude following a scenario similar to Eckhaus instability in spatially extended systems. We find quantitative agreements between experiments and numerical simulations. The linear stability of the square waves is substantiated analytically by determining the stable fixed points of a map.

Pattern reverberation in networks of excitable systems with connection delays

We consider the recurrent pulse-coupled networks of excitable elements with delayed connections, which are inspired by the biological neural networks. If the delays are tuned appropriately, the network can either stay in the steady resting state, or alternatively, exhibit a desired spiking pattern. It is shown that such a network can be used as a pattern-recognition system. More specifically, the application of the correct pattern as an external input to the network leads to a self-sustained reverberation of the encoded pattern. In terms of the coupling structure, the tolerance and the refractory time of the individual systems, we determine the conditions for the uniqueness of the sustained activity, i.e., for the functionality of the network as an unambiguous pattern detector. We point out the relation of the considered systems with cyclic polychronous groups and show how the assumed delay configurations may arise in a self-organized manner when a spike-time dependent plasticity of the connection delays is assumed. As excitable elements, we employ the simplistic coincidence detector models as well as the Hodgkin-Huxley neuron models. Moreover, the system is implemented experimentally on a Field-Programmable Gate Array.