# Louis M. PecoraUnited States Naval Research Laboratory | NRL

Louis M. Pecora

## About

156

Publications

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Citations since 2016

Introduction

## Publications

Publications (156)

A recent paper by R. Muolo, T. Carletti, J. P. Gleeson, and M. Asllani [Entropy 23, 36 (2021)] presents a mainly numerical study on the role of non-normality in the synchronization of coupled periodic oscillators, deriving apparent contradictions with the existing literature. Here, we show that their conclusions are artifactual due to a misinterpre...

The topology of a network associated with a reservoir computer is often taken so that the connectivity and the weights are chosen randomly. Optimization is hardly considered as the parameter space is typically too large. Here we investigate this problem for a class of reservoir computers for which we obtain a decomposition of the reservoir dynamics...

Symmetries are an essential feature of complex networks as they regulate how the graph collective dynamics organizes into clustered states. We here show how to control network symmetries, and how to enforce patterned states of synchronization with nodes clustered in a desired way. Our approach consists of perturbing the original network connectivit...

Symmetries are an essential feature of complex networks as they regulate how the graph collective dynamics organizes into clustered states. We here show how to control network symmetries, and how to enforce patterned states of synchronization with nodes clustered in a desired way. Our approach consists of perturbing the original network connectivit...

Real-world systems in epidemiology, social sciences, power transportation, economics and engineering are often described as multilayer networks. Here we first define and compute the symmetries of multilayer networks, and then study the emergence of cluster synchronization in these networks. We distinguish between independent layer symmetries which...

Real-world systems in epidemiology, social sciences, power transportation, economics and engineering are often described as multilayer networks. Here we first define and compute the symmetries of multilayer networks, and then study the emergence of cluster synchronization in these networks. We distinguish between independent layer symmetries, which...

While there has been considerable work addressing consensus and group consensus in single-layer networks, not much attention has been devoted to consensus in multilayer networks. In this paper, we fill this gap by considering multilayer networks consisting of agents of different types while agents of the same type are arranged in individual layers....

A reservoir computer is a complex nonlinear dynamical system that has been shown to be useful for solving certain problems, such as prediction of chaotic signals, speech recognition, or control of robotic systems. Typically, a reservoir computer is constructed by connecting a large number of nonlinear nodes in a network, driving the nodes with an i...

There has been substantial work studying consensus problems for which there is a single common final state, although there are many real-world complex networks for which the complete consensus may be undesirable. More recently, the concept of group consensus whereby subsets of nodes are chosen to reach a common final state distinct from others has...

There has been substantial work studying consensus problems for which there is a single common final state, although there are many real-world complex networks for which the complete consensus may be undesirable. More recently, the concept of group consensus whereby subsets of nodes are chosen to reach a common final state distinct from others has...

A reservoir computer is a complex nonlinear dynamical system that has been shown to be useful for solving certain problems, such as prediction of chaotic signals, speech recognition or control of robotic systems. Typically a reservoir computer is constructed by connecting a large number of nonlinear nodes in a network, driving the nodes with an inp...

We investigate cluster synchronization in experiments with a multilayer network of electronic Colpitts oscillators, specifically a network with two interaction layers. We observe and analytically characterize the appearance of several cluster states as we change coupling in the layers. In this study, we innovatively combine bifurcation analysis and...

We study cluster synchronization in networks and show that the stability of all possible cluster synchronization patterns depends on a small set of Lyapunov exponents. Our approach can be applied to clusters corresponding to both orbital partitions of the network nodes (symmetry-cluster synchronization) and equitable partitions of the network nodes...

Complex networks are the subject of fundamental interest from the scientific community at large. Several metrics have been introduced to characterize the structure of these networks, such as the degree distribution, degree correlation, path length, clustering coefficient, centrality measures etc. Another important feature is the presence of network...

Synchronization is a collective phenomenon that appears in many natural and man-made networks of oscillators or dynamical systems such as telecommunication, neuronal and biological networks. An interesting form of synchronization is cluster synchronization where the network becomes partitioned into groups of oscillator nodes which synchronize to ea...

We study cluster synchronization in networks with symmetries in the presence of small generic parametric mismatches of two different types: mismatches affecting the dynamics of the individual uncoupled systems and mismatches affecting the network couplings. We perform a stability analysis of the nearly synchronous cluster synchronization solution a...

The study of synchronization of coupled systems is currently undergoing a major surge fueled by recent discoveries of new forms of collective dynamics and the development of techniques to characterize a myriad of new patterns of network synchronization. This includes chimera states, phenomena determined by symmetry, remote synchronization, and asym...

Synchronization is an important and prevalent phenomenon in natural and engineered systems. In many dynamical networks, the coupling is balanced or adjusted in order to admit global synchronization, a condition called Laplacian coupling. Many networks exhibit incomplete synchronization, where two or more clusters of synchronization persist, and com...

Synchronization is an important phenomenon in complex networks of oscillators
and many patterns of synchronized clusters result from symmetries in the
network and the related equations of motion. Application of computational group
theory has proved invaluable in discovering these clusters and analyzing their
stability. However, in some networks, es...

Synchronization is of central importance in power distribution,
telecommunication, neuronal, and biological networks. Many networks are
observed to produce patterns of synchronized clusters, but it has been
difficult to predict these clusters or understand the conditions under which
they form, except for in the simplest of networks. In this article...

Chaos has long been recognized to be generally advantageous from the perspective of control. In particular, the infinite number of unstable periodic orbits embedded in a chaotic set and the intrinsically sensitive dependence on initial conditions imply that a chaotic system can be controlled to a desirable state by using small perturbations. Invest...

Recent numerical experiments of Pecora et al. [Phys. Rev. E 83, 065201 (2011)] have investigated tunneling between two-dimensional symmetric double wells separated by a tunneling barrier. The wells were bounded by hard walls and by the potential barrier which was created by a step increase from the zero potential within a well to a uniform barrier...

We solve the Dirac equation in two spatial dimensions in the setting of resonant tunneling, where the system consists of two symmetric cavities connected by a finite potential barrier. The shape of the cavities can be chosen to yield both regular and chaotic dynamics in the classical limit. We find that certain pointer states about classical period...

We study tunneling in various shaped, closed, two-dimensional, flat
potential, double wells by calculating the energy splitting between symmetric
and anti-symmetric state pairs. For shapes that have regular or nearly regular
classical behavior (e.g. rectangular or circular) the tunneling rates vary
greatly over wide ranges often by several orders o...

We propose a scheme to modulate quantum transport in nanostructures based on classical chaos. By applying external gate voltage to generate a classically forbidden region, transient chaos can be generated, and the escape rate associated with the underlying non-attracting chaotic set can be varied continuously by adjusting the gate voltage. We demon...

In a chain of mutually coupled oscillators, the coupling threshold for synchronization between the outermost identical oscillators decreases when a type of impurity (in terms of parameter mismatch) is introduced in the inner oscillator(s). The outer oscillators interact indirectly via dynamic relaying, mediated by the inner oscillator(s). We confir...

In a chain of mutually coupled oscillators, the coupling threshold for synchronization between the outermost identical oscillators decreases when a type of impurity (in terms of parameter mismatch) is introduced in the inner oscillator(s). The outer oscillators interact indirectly via dynamic relaying, mediated by the inner oscillator(s). We confir...

We solve the Dirac equation in two spatial dimensions in the setting of
resonant tunneling, where the system consists of two symmetric cavities
connected by a finite potential barrier. The shape of the cavities can
be chosen to yield both regular and chaotic dynamics in the classical
limit. We find that certain pointer states about classical period...

Some monitoring programs for ecological resources are developed as components of larger science or management programs and
are thus guided by a priori hypotheses. More commonly, ecological monitoring programs are initiated for the purpose of surveillance
with no a priori hypotheses in mind. No conceptual framework currently exists to guide the deve...

Quantum tunneling rates through a barrier separating two-dimensional, symmetric, double-well potentials are shown to depend on the classical dynamics of the billiard trajectories in each well and, hence, on the shape of the wells. For shapes that lead to regular (integrable) classical dynamics the tunneling rates fluctuate greatly with eigenenergie...

Weakly chaotic or weakly interacting systems have a wide regime where the common random matrix theory modeling does not apply. As an example we consider cold atoms in a nearly integrable optical billiard with a displaceable wall (piston). The motion is completely chaotic but with a small Lyapunov exponent. The Hamiltonian matrix does not look like...

Chaotic systems, that have a small Lyapunov exponent, do not obey the common random matrix theory predictions within a wide "weak quantum chaos" regime. This leads to a novel prediction for the rate of heating for cold atoms in optical billiards with vibrating walls. The Hamiltonian matrix of the driven system does not look like one from a Gaussian...

Master-stability functions (MSFs) are fundamental to the study of synchronization in complex dynamical systems. For example, for a coupled oscillator network, a necessary condition for synchronization to occur is that the MSF at the corresponding normalized coupling parameters be negative. To understand the typical behaviors of the MSF for various...

It is known that chaos-assisted dynamical tunneling may occur in nonintegrable (chaotic) systems. Recently we investigate wave chaotic systems to see if the system may promote the chaos-assisted spatial tunneling in addition to the dynamic tunneling. Our previous experiments suggest some enhancement of the spatial tunneling rate in a coupled, wave-...

In the analysis of complex, nonlinear time series, scientists in a variety of disciplines have relied on a time delayed embedding of their data, i.e., attractor reconstruction. The process has focused primarily on intuitive, heuristic, and empirical arguments for selection of the key embedding parameters, delay and embedding dimension. This approac...

IntroductionMethods of Detecting Coupling Cross-CorrelationMutual InformationMutual Information in Two DimensionsPhase CorrelationContinuity MeasureLinear and Nonlinear Systems Gaussian Distributed White NoiseAutoregressive ModelHénon MapRössler AttractorCircuit DataUncoupled Systems Correlation Between Gaussian Distributed Random Data SetsCorrelat...

Given a sampling of pairs of points from a function’s domain and range, what can we say about the mathematical properties, if any, of that function? For example, were the point pairs related by a function that is continuous? Or differentiable? This is the same situation we are faced with when we apply standard statistical tools, like linear correla...

Starting from an initial wiring of connections, we show that the synchronizability of a network can be significantly improved by evolving the graph along a time dependent connectivity matrix. We consider the case of connectivity matrices that commute at all times, and compare several approaches to engineer the corresponding commutative graphs. In p...

Introduction and MotivationThe Geometry of Synchronization Simple ExamplesSome Generalizations and a Definition of Identical SynchronizationThe Dynamics of Synchronization Stability and the Transverse ManifoldSynchronizing Chaotic Systems, Variations on ThemesSynchronous Circuits and ApplicationsStability and Bifurcations of Synchronized, Mutually...

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We investigate the use of a vibrational approach for the detection of barely visible impact damage in a composite UAV wing. The wing is excited by a shaker according to a predetermined signal, and the response is observed by a system of fiber Bragg grating strain sensors. We use two different driving sequences: a stochastic signal consisting of whi...

We recently showed that the seemingly separate problems of finding a proper time delay and then finding a proper embedding dimension for attractor reconstruction are really the same problem which can be solved with a mathematical statistic faithful to the Takens reconstruction theorem. This approach also deals well with disparate time scales in dat...

In this work we develop a numerical test for Holder continuity and apply it and another test for continuity to the difficult problem of detecting damage in structures. We subject a thin metal plate with incremental damage to the plate changes, its filtering properties, and therefore the phase space trajectories of the response chaotic excitation of...

In this work, recent advances in the use of nonlinear time-series analysis for structural health monitoring are extended to incorporate multivariate data. Structural response data recorded at multiple locations are combined using a multivariate time delay embedding in order to reconstruct the structure's dynamical attractor. Using this approach, a...

Reconstruction of attractors for dynamical systems has typically focused
on solving seemingly separate problems of finding a proper time delay
and then finding a proper embedding dimension. Techniques for solving
these problems are somewhat heuristic. We show that the two problems of
time delay and embedding dimension are actually the same problem....

A number of important questions in ecology involve the possibility of interactions or "coupling" among potential components of ecological systems. The basic question of whether two components are coupled (exhibit dynamical interdependence) is relevant to investigations of movement of animals over space, population regulation, food webs and trophic...

Theory of identical or complete synchronization of identical oscillators in arbitrary networks is introduced. In addition,
several graph theory concepts and results that augment the synchronization theory and a tie in closely to random, semirandom,
and regular networks are introduced. Combined theories are used to explore and compare three types of...

We describe an experiment using a chaotically driven metal plate with incremental damage. Damage in the plate is manifested as a local change in the plate's response (loss of stiffness). We develop a statistical test for Holder continuity and demonstrate its use by examining the map between responses of the undamaged plate and responses of the dama...

A rigorous analytical approach is developed to test for the existence of a continuous nonlinear functional relationship between systems. We compare the application of this nonlinear local technique to the existing analytical linear global approach in the setting of increasing additive noise. For natural systems with unknown levels of noise and nonl...

Recent works by Nichols et al. (Nichols, J.M., Todd, M.D., Seaver, M. and Virgin, L.N. (2003). Use of chaotic excitation and attractor property analysis in structural health monitoring. Phys Rev E, 67(016209)) and Pecora et al. (Todd, M.D., Nichols, J.M., Pecora, L.M. and Virgin, L.N. (2001). Vibration-based damage assessment utilizing state-space...

The Kaplan-Yorke conjecture suggests a simple relationship between the fractal dimension of a system and its Lyapunov spectrum. This relationship has important consequences in the broad field of nonlinear dynamics where dimension and Lyapunov exponents are frequently used descriptors of system dynamics. We develop an experimental system with contro...

We employ chaotic interrogation of a circuit simulation of a structure in order to test for damage to the structure. The circuit simulation provides a realistic test of our attractor-based method and permits close control over parameters in the structure. In this circuit, simulating an eight-degree-of-freedom spring-mass system, we were able to det...

Analysis of data from experiments on dynamical systems often centers on the embedding of time series data to reconstruct an atttractor. In our system, we consider output expressed as multiple time series from a circuit designed to simulate a spring-mass system in both an undamaged and a damaged state. In order to analyze differences in the reconstr...

Many experiments have the ability to record more than one time series of data simultaneously. We explore two issues that are present when multiple time series are used to reconstruct attractors which are not present in the case of one time series. First, we show that there is an algorithmic approach to false nearest neighbors that naturally extends...

Whether epileptic seizures can be predicted by quantitative analysis methods applied to EEG has been a focus of much recent interest [740,751,752]. This resurgence of interest has been motivated by several factors, including the proliferation of powerful new methods for analyzing nonlinear system dynamics, as well as interest in developing epilepsy...

One of the classic problems in the study of nonlinear dynamics has been the diode resonator. Previous work with the diode resonator sought to explain the causes of period doubling and chaos, and often used simplified models. This paper instead seeks to link the onset of nonlinear dynamical effects to measurable parameters by comparing experiments a...

We quantify the dynamical implications of the small-world phenomenon by considering the generic synchronization of oscillator networks of arbitrary topology. The linear stability of the synchronous state is linked to an algebraic condition of the Laplacian matrix of the network. Through numerics and analysis, we show how the addition of random shor...

A method for reconstructing dimensions of subspaces for weakly coupled dynamical systems is offered. The tool is able to extrapolate the subspace dimensions from the zero coupling limit, where the division of dimensions as per the algorithm is exact. Implementation of the proposed technique to multivariate data demonstrates its effectiveness in dis...

A novel feature extracted from a nonlinear time series is presented within the context of vibration-based damage detection in a system. An eight-degree-of-freedom spring-mass-damper `structure' is considered with damage incurred by a stiffness degradation in one spring. The system is excited with a chaotic input, and by tuning the Lyapunov exponent...

We describe a method to characterize the predictability and functionality between two simultaneously generated time series. This nonlinear method requires minimal assumptions and can be applied to data measured either from coupled systems or from different positions on a spatially extended system. This analysis generates a function statistic, Theta...

When thin films of yttrium iron garnet (YIG) are placed in a magnetic field and driven at microwave (rf) frequencies, nonlinear interactions within the material cause the normal microwave spin precession to be modulated at lower frequencies. We measure these lower frequency (kHz) signals at two spatially separated locations on the YIG film and use...

A definition of synchronization of coupled dynamical systems is provided. We discuss how such a definition allows one to identify a unifying framework for synchronization of dynamical systems, and show how to encompass some of the different phenomena described so far in the context of synchronization of chaotic systems.

Recently proposed methodologies in the field of vibration- based structural health monitoring have focused on the incorporation of statistical-based analysis. The structure in question is dynamically excited, some feature is identified for extraction from a measured data set, and that feature is classified as coming from a damaged or undamaged stru...

For patients with medically intractable epilepsy, there have been few effective alternatives to resective surgery, a destructive, irreversible treatment. A strategy receiving increased attention is using interictal spike patterns and continuous EEG measurements from epileptic patients to predict and ultimately control seizure activity via chemical...