John L Hudson

University of Virginia | UVa

Experiments and supporting theoretical analysis is presented to describe the synchronization patterns that can be observed with a population of globally coupled electrochemical oscillators close to a homoclinic, saddle-loop bifurcation, where the coupling is repulsive in the electrode potential. While attractive coupling generates phase clusters an...

Experiments and supporting theoretical analysis are presented to describe the synchronization patterns that can be observed with a population of globally coupled electrochemical oscillators close to a homoclinic, saddle-loop bifurcation, where the coupling is repulsive in the electrode potential. While attractive coupling generates phase clusters a...

A theoretical analysis is presented to show the general occurrence of phase clusters in weakly, globally coupled oscillators close to a Hopf bifurcation. Through a reductive perturbation method, we derive the amplitude equation with a higher order correction term valid near a Hopf bifurcation point. This amplitude equation allows us to calculate an...

A method, apparatus, and computer program product for controlling the behavior of complex rhythmic systems, such as the nervous system, is disclosed. Robust, engineering based measurements of the rhythmic system are taken and used to generate feedback that guides the system towards a desired state. This methodically designed feedback allows the sys...

Background Infants admitted to the neonatal intensive care unit (NICU), and especially those born with very low birth weight (VLBW; <1500 grams), are at risk for respiratory decompensation requiring endotracheal intubation and mechanical ventilation. Intubation and mechanical ventilation are associated with increased morbidity, particularly in urge...

In healthy neonates, connections between the heart and lungs through brain stem chemosensory pathways and the autonomic nervous system result in cardiorespiratory synchronization. This interdependence between cardiac and respiratory dynamics can be difficult to measure because of intermittent signal quality in intensive care settings and variabilit...

We experimentally demonstrate the use of continuous, time-delayed, feedback stimulation for controlling the synchronization of neuron action potentials. Phase-based models were experimentally constructed from a single synaptically isolated cultured hippocampal neuron. These models were used to determine the stimulation parameters necessary to produ...

Komplexe dynamische Strukturen gezielt wählen: Ein Ensemble aus 64 chemischen chaotischen Oszillatoren (Phasenraummomentaufnahmen, links), das die elektrochemische Auflösung von Nickel beschreibt, wird zur Bildung von Ein- (Mitte) und Zwei-Clusterzuständen (rechts) bei mildem globalem Feedback geführt.

Phase models are a powerful method to quantify the coupled dynamics of nonlinear oscillators from measured data. We use two phase modeling methods to quantify the dynamics of pairs of coupled electrochemical oscillators, based on the phases of the two oscillators independently and the phase difference, respectively. We discuss the benefits of the t...

The collective behavior of populations of rhythmic processes is important in a variety of fields including chemistry (influence on overall rate of reaction, pitting corrosion), biology (circadian rhythms, synchrony associated with epileptic seizures), and engineering (lasers and microwave systems). The focus of the presentation is on experiments wi...

a b s t r a c t Effects of pulse stimulations on the dynamics of relaxation oscillator populations were experimentally studied in a globally coupled electrochemical system. Similar to smooth oscillations, weakly and moderately relaxational oscillations possess a vulnerable phase, φ S ; pulses applied at φ S resulted in desynchronization followed by...

A mild, nonlinear, time-delayed feedback signal was applied to two heterogeneous oscillators in order to synchronize their frequencies with an arbitrary and controllable phase difference. The feedback was designed using phase models constructed from experimental measurements of the intrinsic dynamical properties of the oscillators. The feedback sig...

We report an experimental and model based study on the effect of negative coupling, induced by adding IR compensation, on bistability, and synchronization behavior of a dual-electrode metal dissolution electrochemical system. We show that, unlike the case of a single electrode, IR compensation cannot be used to remove bistability; with a large IR c...

We have developed an engineering framework which utilizes experiment-based phase models to tune complex dynamic structures to desired states; weak, non-destructive signals are employed to alter interactions among nonlinear rhythmic elements. In this manuscript we present an integrated overview and discussion of our recent studies in this area. Expe...

Collective organization, such as rhythmic patterns and synchronized states, is commonly found in complex systems composed of a large number of interacting oscillatory elements. Such behavior is important in biological functions such as circadian rhythm and memory as well as in epilepsy and essential tremors. A major question of both theoretical and...

A new approach is presented for the reconstruction of phase synchronization phenomena from measurement data of two coupled chaotic oscillators. The oscillators are assumed to be non–phase-coherent, making the synchronization analysis extremely difficult. To deal with such non–phase-coherent systems, a CPR index has been recently developed based on...

A method for engineering the global behavior of populations of rhythmic elements is presented. The framework, which is based on phase models, allows a nonlinear time-delayed global feedback signal to be constructed which produces an interaction function corresponding to the desired behavior of the system. It is shown theoretically and confirmed in...

A method for engineering the behavior of populations of rhythmic elements is presented. The framework, which is based on phase models, allows a nonlinear time-delayed global feedback signal to be constructed which produces an interaction function corresponding to the desired behavior of the system. It is shown theoretically and confirmed in numeric...

Control of collective dynamics with global time-delayed feedback was experimentally studied with (phase) synchronized populations of smooth, relaxational, and chaotic electrochemical oscillators. The experimental results provide laboratory evidence for the findings in the studies of delayed feedback on phase oscillators; multiple, isolated regions...

Experiments are carried out with a globally coupled, externally forced population of limit-cycle electrochemical oscillators with an approximately unimodal distribution of heterogeneities. Global coupling induces mutually entrained (at frequency omega1) states; periodic forcing produces forced-entrained (omegaF) states. As a result of the interacti...

Experiments are carried out with a globally coupled, externally forced population of limit-cycle electrochemical oscillators with an approximately unimodal distribution of heterogeneities. Global coupling induces mutually entrained (at frequency $\omega_{1}$) states; periodic forcing produces forced-entrained ($\omega_{\mathrm{F}}$) states. As a re...

We investigate the emergence of synchronization in two groups of oscillators; one group acts as a synchronization source, and the other as the target. Based on phase model simulations, we construct a synchrony index (SI): a combination of intra- and intergroup synchronies. The SI characterizes the extent of induced synchrony in the population. We d...

An approach is presented for extracting phase equations from multivariate time series data recorded from a network of weakly coupled limit cycle oscillators. Our aim is to estimate important properties of the phase equations including natural frequencies and interaction functions between the oscillators. Our approach requires the measurement of an...

A previously developed spatiotemporal model of the interactions among metastable pits on homogeneous electrodes is extended to heterogeneous surfaces with randomly distributed inclusion sites in an otherwise passive electrode. The inclusions are treated as favored sites for pit initiation events. The effect of the spatial density of inclusions on s...

We used phase models to describe and tune complex dynamic structures to desired states; weak, nondestructive signals are used to alter interactions among nonlinear rhythmic elements. Experiments on electrochemical reactions on electrode arrays were used to demonstrate the power of mild model-engineered feedback to achieve a desired response. Applic...

A novel approach is presented for extracting phase equations from multivariate time series data recorded from a network of weakly coupled limit cycle oscillators. Our aim is to estimate all the important properties of the phase equations such as natural frequencies and interaction function between the oscillators. Our approach requires the measurem...

Stochastic temporal and spatiotemporal models of metastable pitting on a metal surface are presented. A stochastic reaction-diffusion model accounts for the effects of local changes in concentration, potential drop, and oxide film damage on the nucleation of subsequent events. The cooperative interactions among events can lead to the formation of c...

Experiments are carried out with a chemical burster, the electrodissolution of iron in sulfuric acid solution. The system exhibits bursting oscillations in which fast periodic spiking is superimposed on chaotic, slow oscillations. Regularization of the slow dynamics, i.e., transition from chaotic to periodic bursting oscillations, is investigated t...

We present two different approaches to detect and quantify phase synchronization in the case of coupled non-phase coherent oscillators. The first one is based on the general idea of curvature of an arbitrary curve. The second one is based on recurrences of the trajectory in phase space. We illustrate both methods in the paradigmatic example of the...

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A spatiotemporal model of metastable pitting at a homogeneous metal surface under potentiostatic conditions is presented. The model accounts for local changes adjacent to metastable pits and their effect on the nucleation of subsequent events. The local changes considered include concentration, potential drop and oxide film damage. The interactions...

We show that mutual entrainment in interacting oscillators can be characterized using phase models that are developed from direct experiments with a single oscillator. The models are used to predict order-disorder transitions in populations and the dependence of order on system parameters; the description is verified in independent experiments in s...

Various stimulation desynchronization techniques are explored in a laboratory experiment on electrochemical oscillators, a system that exhibits transient dynamics, heterogeneities, and inherent noise. Stimulation with a short, single pulse applied at a vulnerable phase can effectively desynchronize a cluster. A double pulse method, that can be appl...

The calculation of order parameters to characterize the degree of synchronization usually requires the measurement of time series of observable quantities for all individual dynamical elements. In this article, a new method of extracting the Kuramoto order from global measurements for weakly coupled, nearly identical oscillators is established and...

Experiments on phase and generalized synchronization of two coupled, nonidentical chaotic electrochemical oscillations are presented. We adapt measures of characterizing synchronization of a non-phase-coherent chaotic behavior and compare its properties and physicochemical mechanism to those of a phase-coherent behavior. Phase synchronization sets...

The electro-catalytic oxidation of CO and CO/H 2 mixtures on polycrystalline Pt has been investigated on two electrodes with controllable degrees of coupling strength by means of experiments and numerical simulations. With strong positive coupling, large differences between the currents of the two almost-identical electrodes arise in a range of pot...

We report experimental and numerical results on noise-enhanced synchronization of two coupled chaotic oscillators. Enhanced synchronization is achieved through superimposing small-amplitude Gaussian noise on a common system parameter of the two chaotic oscillators. A resonancelike behavior is found: at an optimum level of noise, maximum synchroniza...

Amplitude death was observed in experiments with two coupled periodic electrochemical oscillators without time delay. Simulation results confirmed that the observed amplitude death was obtained via a Hopf bifurcation. The two oscillators must have a minimum discrepancy and both be near their individual Hopf bifurcations for amplitude death to occur...

Experiments on an array of 64 globally coupled chaotic electrochemical oscillators were carried out. The array is heterogeneous due to small variations in the properties of the electrodes and there is also a small amount of noise. Over some ranges of the coupling parameter, dynamical clustering was observed. The precision-dependent cluster configur...

Numerical and experimental evidences are presented to show that many phase synchronized systems of nonidentical chaotic oscillators, where the chaotic state is reached through a period-doubling cascade, show rapid convergence of the time-averaged frequency. The speed of convergence toward the natural frequency scales as the inverse of the measureme...

We present numerical studies on pattern formation in the excitable region of an electrochemical model that was originally proposed to reproduce nonlinear phenomena observed during the dissolution of metals that exhibit an active–passive transition. The simulations are done employing a realistic three-dimensional geometry of the electrochemical cell...

Experiments on the collective behavior and phase synchronization of weakly coupled populations of non-identical chaotic electrochemical oscillators are described. Without added coupling no deviation from the law of large numbers of the mean field is observed with increasing system size. Deviations do arise with very weak global or short-range coupl...

We report experiments on emerging coherence through weak global coupling of populations of electrochemical oscillators with heterogeneities. The experiments are done with an array of nickel electrodes undergoing electrodissolution in sulfuric acid. The experiments verify theories of Winfree and Kuramoto that predict that global coupling of a set of...

Experiments were carried out on bursting oscillations in an electrochemical system, the dissolution of iron in sulfuric acid. Bursting characteristics were investigated as functions of the parameters applied potential and external resistance. We develop a model that incorporates the effects of oxide and salt films. This model reproduces all the imp...

Pattern formation in electrochemical systems depends sensitively on the relative arrangement of the electrodes. We present simulations of spatiotemporal patterns during the electrodissolution of a metal disk electrode in which the reference electrode is located on the axis of the disk and close to the metal working electrode. This geometry introduc...

Numerical and experimental evidence is presented to show that many phase synchronized systems of non-identical chaotic oscillators, where the chaotic state is reached through a period-doubling cascade, show rapid convergence of the time-averaged frequency. The speed of convergence toward the natural frequency scales as the inverse of the measuremen...

Experimental and numerical evidence of coherence resonance in an electrochemical system is reported. External noise with a Gaussian distribution is superimposed on the system when the anodic current is exhibiting stationary (fixed point) dynamics below a supercritical Hopf bifurcation. The amplitude of the added stochastic perturbations is increase...

The effect of noise on phase synchronization in small sets and larger populations of weakly coupled chaotic oscillators is explored. Both independent and correlated noise are found to enhance phase synchronization of two coupled chaotic oscillators below the synchronization threshold; this is in contrast to the behavior of two coupled periodic osci...

We propose a method for the determination of a characteristic oscillation frequency for a broad class of chaotic oscillators generating complex signals. It is based on the locking of standard periodic self-sustained oscillators by an irregular signal. The method is applied to experimental data from chaotic electrochemical oscillators, where other a...

Experiments on the collective behavior and phase synchronization of weakly coupled populations of nonidentical chaotic electrochemical oscillators are described. The weak coupling has only a small effect on the local dynamics, i.e., through changes in frequency, but it has a strong influence on the collective or overall behavior. With added weak gl...

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

Experiments on the collective dynamics and phase synchronization of populations of identical chaotic electrochemical oscillators were presented. No deviation from the law of large numbers was observed without added coupling. The variation of mean field oscillation with the number of elements for both weak global and short-range coupling was investi...

Coherence of interacting oscillating entities has importance in biological, chemical, and physical systems. We report experiments on populations of chemical oscillators and verify a 25-year-old theory of Kuramoto that predicts that global coupling in a set of smooth limit-cycle oscillators with different frequencies produces a phase transition in w...

First published as an Advance Article on the web 9th May 2002 Experiments on two coupled chaotic electrochemical oscillators with different frequencies are presented. We consider two types of coupling. The first is imposed through a set of external resistors. The second arises from the potential drop in the electrolyte and generally depends on cell...

Interactions among local pit sites were investigated using a 5×5 array of 25 electrodes consisting of closely spaced, flush-mounted 316 stainless steel wires. Three types of interactions occurred when actively corroding pits existed while the remaining electrodes were initially passive in 0.05 M NaCl solution. Suppression of pitting on nearby elect...

Spatiotemporal patterns including accelerating fronts, rotating waves, and homogeneous oscillations evolve during the electrodissolution of metals like cobalt and iron that exhibit passivity under potentiostatic control. The nature of the patterns is determined by long-range (nonlocal) coupling through the electric field which in turn is influenced...

Experiments were carried out on arrays of chaotic electrochemical oscillators to which global coupling, periodic forcing, and feedback were applied. The global coupling converts a very weakly coupled set of chaotic oscillators to a synchronized state with sufficiently large values of coupling strength; at intermediate values both intermittent and s...

Experiments on chaotically oscillating arrays of nickel electrodes in sulfuric acid were carried out. A global feedback is added in which a signal proportional to the difference between the sum of the currents of all elements and a mean current is fed back to the applied potential. The addition of global feedback transforms a system of weakly coupl...

Spatiotemporal patterns on a disk electrode are simulated with a model for the electrodissolution of a metal that exhibits passivity; a 3-dimensional geometry with a point reference electrode is used. The two variables of the model are the potential drop across the electric double layer and the proton concentration near the surface of the working e...

Spatiotemporal patterns that appear during the electrodissolution of a metal that exhibits passivity are simulated by a two-variable model in a three-dimensional geometry with a point like reference electrode. The dynamical variables of the model are the potential drop across the electric double layer and the proton concentration in front of the wo...

Experiments were carried out on synchronization and control of complex chaotic dynamics observed during the dissolution of two and four coupled nickel electrodes in sulfuric acid under potentiostatic conditions. In a given potential range the individually measured currents exhibit asynchronous chaotic oscillations. The complexity (as measured by th...

A model for the simulation of experimentally observed spatiotemporal patterns in the bistable and oscillatory regions during the electrodissolution of metals under potentiostatic control is presented. A two-dimensional geometry was used with a point-like reference electrode located in the electrolyte between the working and the counter electrodes....

Experiments on the dynamic behavior of some electrochemical reactions, with emphasis on metal dissolution, are discussed. Although patterns occur in the bistable, excitable, and periodic and chaotic oscillatory regions, we limit this presentation to the latter case. Emphasis is given to the importance of coupling of local reaction sites, in this ca...

Interactions among small sets of two to eight nickel electrodes undergoing chaotic electrodissolution in sulfuric acid were studied. A single oscillator under these conditions exhibits low-dimensional chaotic behavior. Global coupling among the electrodes was added with the use of external resistors in a manner such that the strength of the couplin...

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The interplay of mass transfer and reaction in two-phase systems exhibiting oscillatory behavior has been investigated. A distributed model, based on partial differential equations describing unsteady mass transfer and reaction at the interface and ordinary differential equations describing reaction in the bulk phases, has been developed. Two react...