Coherence of interacting oscillating entities has importance in biological, chemical, and physical systems. We report experiments on populations chemical oscillators verify a 25-year-old theory Kuramoto that predicts global coupling set smooth limit-cycle with different frequencies produces phase transition which some the elements synchronize. Both critical point predicted dependence order are seen experiments. extend studies both to relaxation chaotic characterize quantitative similarities...

Dynamical processes in many engineered and living systems take place on complex networks of discrete dynamical units. We present laboratory experiments with a networked chemical system nickel electrodissolution which synchronization patterns are recorded smooth periodic, relaxation chaotic oscillators organized composed up to twenty units 140 connections. The reaction formed domains that strongly affected by the architecture network. Spatially partial could be observed either due densely...

We used phase models to describe and tune complex dynamic structures desired states; weak, nondestructive signals are alter interactions among nonlinear rhythmic elements. Experiments on electrochemical reactions electrode arrays were demonstrate the power of mild model-engineered feedback achieve a response. Applications made generation sequentially visited cluster patterns similar reproducible sequences seen in biological systems design antipacemaker for destruction pathological...

Experiments on chaotically oscillating arrays of 64 nickel electrodes in sulfuric acid were carried out. External resistors parallel and series are added to vary the extent global coupling among oscillators without changing other properties system. The array is heterogeneous due small variations there also a amount noise. addition transforms system independent elements state complete synchronization. At intermediate strengths stable clusters, or condensates elements, form. All cluster follow...

We present a new method to detect phase as well generalized synchronization in wide class of complex systems. It is based on the recurrences system's trajectory neighborhood former state space. illustrate applicability algorithm for paradigmatic chaotic Rössler system funnel regime and noisy data, where other methods fail. Furthermore, we demonstrate electrochemical experiments that can easily non-phase-coherent even non-stationary time series.

Abstract Oscillatory behaviour is essential for proper functioning of various physical and biological processes. However, diffusive coupling capable suppressing intrinsic oscillations due to the manifestation phenomena amplitude oscillation deaths. Here we present a scheme revoke these quenching states in diffusively coupled dynamical networks, demonstrate approach experiments with an oscillatory chemical reaction. By introducing simple feedback factor coupling, show that stable...

We show that mutual entrainment in interacting oscillators can be characterized using phase models are developed from direct experiments with a single oscillator. The used to predict order-disorder transitions populations and the dependence of order on system parameters; description is verified independent sets chemical oscillators. experiment-based model properly describes in-phase antiphase positive negative interactions small as well dynamical clustering

The effects of noise on phase synchronization (PS) coupled chaotic oscillators are explored. In contrast to periodic oscillators, is found enhance significantly below the threshold PS. This constructive role has been verified experimentally with electrochemical electrodissolution Ni in sulfuric acid solution.

For many biological and engineered systems, a central function or design goal is to abbreviate the time required synchronize rhythmic process an external forcing signal. We present theory for deriving input that effectively minimizes average transient entrain phase model, which enables practical technique constructing fast entrainment waveforms general nonlinear oscillators. This result verified in numerical simulations using Hodgkin-Huxley neuron experiments on oscillatory electrochemical system.

A theory for obtaining waveform the effective entrainment of a weakly forced oscillator is presented. Phase model analysis combined with calculus variation to derive which an achieved minimum power forcing signal. Optimal waveforms are calculated from phase response curve and solution balancing condition. The tested in chemical experiments oscillations close further away Hopf bifurcation exhibited sinusoidal higher harmonic nontrivial optimal waveforms, respectively.

Abstract The ability to organize and finely manipulate the hierarchy timing of dynamic processes is important for understanding influencing brain functions, sleep metabolic cycles, many other natural phenomena. However, establishing spatiotemporal structures in biological oscillator ensembles a challenging task that requires controlling large collections complex nonlinear dynamical units. In this report, we present method design entrainment signals create stable phase patterns heterogeneous...

Modern Networked Critical Infrastructures (NCI), involving cyber and physical systems, are exposed to intelligent attacks targeting the stable operation of these systems. In order ensure anomaly awareness, observed data can be used in accordance with mining techniques develop Intrusion Detection Systems (IDS) or Anomaly (ADS). There is an increase volume sensor generated by both sensors, so there a need apply Big Data technologies for real-time analysis large sets. this paper, we propose...

Oscillatory Ni dissolution reaction in a nonlocally coupled network of sites produces chimera pattern.

We present a fully automated method for the optimal state space reconstruction from univariate and multivariate time series. The proposed methodology generalizes delay embedding procedure by unifying two promising ideas in symbiotic fashion. Using non-uniform delays allows successful of systems inheriting different scales. In contrast to established methods, minimization an appropriate cost function determines dimension without using threshold parameter. Moreover, is capable detecting...

We report numerical and experimental results indicating successful stabilization of unstable steady states periodic orbits in an electrochemical system. Applying a continuous delayed-feedback technique not only chaotic oscillations are suppressed via steady-state solutions but also the dynamics can be converted to behavior. In all cases feedback perturbation vanishes as target state is attained.

An approach is presented for extracting phase equations from multivariate time series data recorded a network of weakly coupled limit cycle oscillators. Our aim to estimate important properties the including natural frequencies and interaction functions between requires measurement an experimental observable oscillators; in contrast with previous methods it does not require measurements isolated single or two-oscillator setups. This noninvasive technique can be advantageous biological...

We propose a method to infer the coupling structure in networks of nonlinear oscillatory systems with multiple time scales. The partial phase synchronization allows us for coupled oscillators one well-defined scale. case scales has remained challenge until now. Here, we introduce recurrence based analysis tackle this challenge. successfully apply proposed model and experimental data from electrochemical oscillators. statistical significance results is evaluated on surrogate hypothesis test.

Modern Process Control Systems (PCS) exhibit an increasing trend towards the pervasive adoption of commodity, off-the-shelf Information and Communication Technologies (ICT). This has brought significant economical operational benefits, but it also shifted architecture PCS from a completely isolated environment to open, "system systems" integration with traditional ICT systems, susceptible computer attacks. In this paper we present novel approach detect cyber attacks targeting measurements...

Significance Inferring connections forms a critical step toward understanding large and diverse complex networks. To date, reliable efficient methods for the reconstruction of network topology from measurement data remain challenge due to high complexity nonlinearity system dynamics. These obstacles also form bottleneck analyzing controlling dynamic structures (e.g., synchrony) collective behavior in such The novel contribution this work is develop unified data-driven approach reliably...

Significance Synchronization among interacting entities is a process that underlies the function of numerous systems, including circadian clocks and laser arrays. It generally believed homogeneity beneficial for synchronization. This work shows theoretically, numerically, experimentally opposite not only possible but also common in systems with interaction delays. In such heterogeneity shown to promote synchronization, even when completely random. finding advances our understanding interplay...

Experiments on periodically oscillating arrays consisting of from one to 64 nickel electrodes in sulfuric acid are carried out. Harmonic and relaxation oscillations that occur respectively two regions parameter space considered. External resistors parallel series added vary the extent global coupling among oscillators. The array is heterogeneous due small variations properties electrodes, there also a amount noise. With no narrow distribution frequency As harmonic oscillators frequencies...

A simple adaptive controller based on a low-pass filter to stabilize unstable steady states of dynamical systems is considered. The reference-free; it does not require knowledge the location fixed point in phase space. topological limitation similar that delayed feedback discussed. We show saddle-type cannot be stabilized by using conventional filter. can overcome an use demonstrated for several physical models, including pendulum driven constant torque, Lorenz system, and electrochemical...

An adaptive dynamic state feedback controller for stabilizing and tracking unknown steady states of dynamical systems is proposed. We prove that the can never be stabilized if system in sum have an odd number real positive eigenvalues. For two-dimensional systems, this topological limitation only unstable focus or node with a stable controller, stabilization saddle requires presence degree freedom loop. The use to stabilize track points (as well as foci) demonstrated both numerically...

Feedback and external forcing are applied to an array of chaotic electrochemical oscillators through variations in the potential. We see transitions from intermittent clusters stable periodic synchronized states as feedback gain amplitude, respectively, varied. With up four observed states. The transition synchronization with occurs by increase size one cluster at expense others.