Selective monostability in multi-stable systems

We propose a robust method that allows a periodic or a chaotic multi-stable system to be transformed to a monostable system at an orbit with dominant frequency of any of the coexisting attractors. Our approach implies the selection of a particular attractor by periodic external modulation with frequency close to the dominant frequency in the power spectrum of a desired orbit and simultaneous annihilation of all other coexisting states by positive feedback, both applied to one of the system parameters. The method does not require any preliminary knowledge of the system dynamics and the phase space structure. The efficiency of the method is demonstrated in both a non-autonomous multi-stable laser with coexisting periodic orbits and an autonomous Rössler-like oscillator with coexisting chaotic attractors. The experiments with an erbium-doped fibre laser provide evidence for the robustness of the proposed method in making the system monostable at an orbit with dominant frequency of any preselected attractor

Inferring the connectivity of coupled oscillators from time-series statistical similarity analysis

A system composed by interacting dynamical elements can be represented by a network, where the nodes represent the elements that constitute the system, and the links account for their interactions, which arise due to a variety of mechanisms, and which are often unknown. A popular method for inferring the system connectivity (i.e., the set of links among pairs of nodes) is by performing a statistical similarity analysis of the time-series collected from the dynamics of the nodes. Here, by considering two systems of coupled oscillators (Kuramoto phase oscillators and Rossler chaotic electronic oscillators) with known and controllable coupling conditions, we aim at testing the performance of this inference method, by using linear and non linear statistical similarity measures. We find that, under adequate conditions, the network links can be perfectly inferred, i.e., no mistakes are made regarding the presence or absence of links. These conditions for perfect inference require: i) an appropriated choice of the observed variable to be analysed, ii) an appropriated interaction strength, and iii) an adequate thresholding of the similarity matrix. For the dynamical units considered here we find that the linear statistical similarity measure performs, in general, better than the non-linear ones.Peer ReviewedPostprint (published version

Experimental implementation of maximally synchronizable networks

Maximally synchronizable networks (MSNs) are acyclic directed networks that maximize synchronizability. In this paper, we investigate the feasibility of transforming networks of coupled oscillators into their corresponding MSNs. By tuning the weights of any given network so as to reach the lowest possible eigenratio lambdaN/lambda2, the synchronized state is guaranteed to be maintained across the longest possible range of coupling strengths. We check the robustness of the resulting MSNs with an experimental implementation of a network of nonlinear electronic oscillators and study the propagation of the synchronization errors through the network. Importantly, a method to study the effects of topological uncertainties on the synchronizability is proposed and explored both theoretically and experimentally.The authors acknowledge J.L. Echenausía-Monroy, V.P. Vera-Ávila, J. Moreno de León, C. Hapo and P.L. del Barrio for assistance in the laboratory, and the support of MINECO (FIS2012-38949-C03-01 and FIS2013-41057-P). One anonymous referee is acknowledged for having provided valuable advice that has influenced our understanding of the origin of the propagation of the synchronization error, and helped us improve the manuscript in several ways. The authors also acknowledge the computational resources, facilities and assistance provided by the Centro computazionale di RicErca sui Sistemi COmplessi (CRESCO) of the Italian National Agency for New Technologies, Energy and Sustainable Economic Development (ENEA). R.S.E. acknowledges Universidad de Guadalajara, CULagos (Mexico) for financial support (PRO-SNI-2015/228069, PROINPEP/005/2014, UDG-CONACyT/I010/163/2014) and CONACyT (Becas Mixtas MZO2015/290842). D.-U. Hwang acknowledges National Institute for Mathematical Sciences (NIMS) funded by the Ministry of Science, ICT & Future Planning (A21501-3)

Enhancing the stability of the synchronization of multivariable coupled oscillators

Synchronization processes in populations of identical networked oscillators are the focus of intense studies in physical, biological, technological, and social systems. Here we analyze the stability of the synchronization of a network of oscillators coupled through different variables. Under the assumption of an equal topology of connections for all variables, the master stability function formalism allows assessing and quantifying the stability properties of the synchronization manifold when the coupling is transferred from one variable to another. We report on the existence of an optimal coupling transference that maximizes the stability of the synchronous state in a network of Rössler-like oscillators. Finally, we design an experimental implementation (using nonlinear electronic circuits) which grounds the robustness of the theoretical predictions against parameter mismatches, as well as against intrinsic noise of the system.Support from Spanish Ministry of Economy and Competitiveness through Projects No. FIS2011-25167, No. FIS2012-38266, and No. FIS2013-41057-P is also acknowledged. A.A. and J.G.G. acknowledge supportfrom the EC FET-Proactive Projects PLEXMATH (GrantNo. 317614) and MULTIPLEX (Grant No. 317532). J.G.G. acknowledges support from MINECO through the Ramón y Cajal program, the Comunidad de Aragón (Grupo FENOL), and the Brazilian CNPq through the PVE project of the Ciencia Sem Fronteiras program. A.A. acknowledges ICREA Academia and the James S. McDonnell Foundation. R.S.E. ac-knowledges Universidad de Guadalajara, CULagos (Mexico) for financial support (OP/PIFI-2013-14MSU0010Z-17-04,PROINPEP-RG/005/2014, UDG-CONACyT/I010/163/2014) and CONACyT (Becas Mixtas MZO2015/290842)

Experimental implementation of a biometric laser synaptic sensor

We fabricate a biometric laser fiber synaptic sensor to transmit information from one neuron cell to the other by an optical way. The optical synapse is constructed on the base of an erbium-doped fiber laser, whose pumped diode current is driven by a pre-synaptic FitzHugh–Nagumo electronic neuron, and the laser output controls a post-synaptic FitzHugh–Nagumo electronic neuron. The implemented laser synapse displays very rich dynamics, including fixed points, periodic orbits with different frequency-locking ratios and chaos. These regimes can be beneficial for efficient biorobotics, where behavioral flexibility subserved by synaptic connectivity is a challenge

Generalized synchronization in relay systems with instantaneous coupling

We demonstrate the existence of generalized synchronization in systems that act as mediators between two dynamical units that, in turn, show complete synchronization with each other. These are the so-called relay systems. Specifically, we analyze the Lyapunov spectrum of the full system to elucidate when complete and generalized synchronization appear. We show that once a critical coupling strength is achieved, complete synchronization emerges between the systems to be synchronized, and at the same point, generalized synchronization with the relay system also arises. Next, we use two nonlinear measures based on the distance between phase-space neighbors to quantify the generalized synchronization in discretized time series. Finally, we experimentally show the robustness of the phenomenon and of the theoretical tools here proposed to characterize it

Experimental and Numerical Study of an Optoelectronics Flexible Logic Gate Using a Chaotic Doped Fiber Laser

In this chapter, we present the experimental and numerical study of an optoelectronics flexible logic gate using a chaotic erbium-doped fiber laser. The implementation consists of three elements: a chaotic erbium-doped fiber laser, a threshold controller, and the logic gate output. The output signal of the fiber laser is sent to the logic gate input as the threshold controller. Then, the threshold controller output signal is sent to the input of the logic gate and fed back to the fiber laser to control its dynamics. The logic gate output consists of a difference amplifier, which compares the signals sent by the threshold controller and the fiber laser, resulting in the logic output, which depends on an accessible parameter of the threshold controller. The dynamic logic gate using the fiber laser exhibits high ability in changing the logic gate type by modifying the threshold control parameter

Knowledge Discovery in Spectral Data by Means of Complex Networks

In the last decade, complex networks have widely been applied to the study of many natural and man-made systems, and to the extraction of meaningful information from the interaction structures created by genes and proteins. Nevertheless, less attention has been devoted to metabonomics, due to the lack of a natural network representation of spectral data. Here we define a technique for reconstructing networks from spectral data sets, where nodes represent spectral bins, and pairs of them are connected when their intensities follow a pattern associated with a disease. The structural analysis of the resulting network can then be used to feed standard data-mining algorithms, for instance for the classification of new (unlabeled) subjects. Furthermore, we show how the structure of the network is resilient to the presence of external additive noise, and how it can be used to extract relevant knowledge about the development of the disease