Takashi Nishikawa

Takashi Nishikawa
Northwestern University | NU · Department of Physics and Astronomy

Ph.D. in Applied Mathematics

About

71
Publications
10,755
Reads
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3,866
Citations
Additional affiliations
June 2018 - present
Northwestern University
Position
  • Professor
June 2012 - May 2018
Northwestern University
Position
  • Professor (Associate)
July 2007 - May 2012
Clarkson University
Education
September 1996 - December 2000
University of Maryland, College Park
Field of study
  • Applied Mathematics

Publications

Publications (71)
Article
Full-text available
An imperative condition for the functioning of a power-grid network is that its power generators remain synchronized. Disturbances can prompt desynchronization, which is a process that has been involved in large power outages. Here we derive a condition under which the desired synchronous state of a power grid is stable, and use this condition to i...
Article
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To understand the formation, evolution, and function of complex systems, it is crucial to understand the internal organization of their interaction networks. Partly due to the impossibility of visualizing large complex networks, resolving network structure remains a challenging problem. Here we overcome this difficulty by combining the visual patte...
Article
Full-text available
Synchronization, in which individual dynamical units keep in pace with each other in a decentralized fashion, depends both on the dynamical units and on the properties of the interaction network. Yet, the role played by the network has resisted comprehensive characterization within the prevailing paradigm that interactions facilitating pairwise syn...
Preprint
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The ability to control network dynamics is essential for ensuring desirable functionality of many technological, biological, and social systems. Such systems often consist of a large number of network elements, and controlling large-scale networks remains challenging because the computation and communication requirements increase prohibitively fast...
Article
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The ability to control network dynamics is essential for ensuring desirable functionality of many technological, biological, and social systems. Such systems often consist of a large number of network elements, and controlling large-scale networks remains challenging because the computation and communication requirements increase prohibitively fast...
Article
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A central issue in the study of large complex network systems, such as power grids, financial networks, and ecological systems, is to understand their response to dynamical perturbations. Recent studies recognize that many real networks show nonnormality and that nonnormality can give rise to reactivity—the capacity of a linearly stable system to a...
Preprint
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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...
Preprint
Large-scale integration of renewables in power systems gives rise to new challenges for keeping synchronization and frequency stability in volatile and uncertain power flow states. To ensure the safety of operation, the system must maintain adequate disturbance rejection capability at the time scales of both rotor angle and system frequency dynamic...
Preprint
We report on a real-time demand response experiment with 100 controllable devices. The experiment reveals several key challenges in the deployment of a real-time demand response program, including time delays, uncertainties, characterization errors, multiple timescales, and nonlinearity, which have been largely ignored in previous studies. To resol...
Article
We report on a real-time demand response experiment with 100 controllable devices. The experiment reveals several key challenges in the deployment of a real-time demand response program, including time delays, uncertainties, characterization errors, multi-timescales, and nonlinearity, which have been largely ignored in previous studies. To resolve...
Article
Large-scale integration of renewables in power systems gives rise to new challenges for keeping synchronization and frequency stability in volatile and uncertain power flow states. To ensure the safety of the operation, the system must maintain adequate disturbance rejection capability at the time scales of both rotor angle and system frequency dyn...
Preprint
Full-text available
Behavioral homogeneity is often critical for the functioning of network systems of interacting entities. In power grids, whose stable operation requires generator frequencies to be synchronized--and thus homogeneous--across the network, previous work suggests that the stability of synchronous states can be improved by making the generators homogene...
Article
Full-text available
Behavioral homogeneity is often critical for the functioning of network systems of interacting entities. In power grids, whose stable operation requires generator frequencies to be synchronized—and thus homogeneous—across the network, previous work suggests that the stability of synchronous states can be improved by making the generators homogeneou...
Article
Full-text available
Complex chemical reaction networks, which underlie many industrial and biological processes, often exhibit non-monotonic changes in chemical species concentrations. Such non-monotonic dynamics are in principle possible even in a linear model if the matrix defining the model is non-normal, as characterized by a necessarily non-orthogonal set of eige...
Preprint
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Symmetry breaking--the phenomenon in which the symmetry of a system is not inherited by its stable states--underlies pattern formation, superconductivity, and numerous other effects. Recent theoretical work has established the possibility of converse symmetry breaking (CSB), a phenomenon in which the stable states are symmetric only when the system...
Preprint
Full-text available
Complex chemical reaction networks, which underlie many industrial and biological processes, often exhibit non-monotonic changes in chemical species concentrations, typically described using nonlinear models. Such non-monotonic dynamics are in principle possible even in linear models if the matrices defining the models are non-normal, as characteri...
Article
Full-text available
Symmetry breaking—the phenomenon in which the symmetry of a system is not inherited by its stable states—underlies pattern formation, superconductivity and numerous other effects. Recent theoretical work has established the possibility of converse symmetry breaking, a phenomenon in which the stable states are symmetric only when the system itself i...
Article
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In the version of this Article originally published, a normalization factor was missing in the function used to create the right side of the plot in Fig. 2b (where β > 2); please see the correction notice for details. © 2018, The Author(s), under exclusive licence to Springer Nature Limited.
Article
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The understanding of cascading failures in complex systems has been hindered by the lack of realistic large-scale modeling and analysis that can account for variable system conditions. Using the North American power grid, we identified, quantified, and analyzed the set of network components that are vulnerable to cascading failures under any out of...
Article
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Cluster synchronization is a phenomenon in which a network self-organizes into a pattern of synchronized sets. It has been shown that diverse patterns of stable cluster synchronization can be captured by symmetries of the network. Here we establish a theoretical basis to divide an arbitrary pattern of symmetry clusters into independently synchroniz...
Article
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A scenario has recently been reported in which in order to stabilize complete synchronization of an oscillator network---a symmetric state---the symmetry of the system itself has to be broken by making the oscillators nonidentical. But how often does such behavior---which we term asymmetry-induced synchronization (AISync)---occur in oscillator netw...
Article
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Traditional studies of chaos in conservative and driven dissipative systems have established a correspondence between sensitive dependence on initial conditions and fractal basin boundaries, but much less is known about the relation between geometry and dynamics in undriven dissipative systems. These systems can exhibit a prevalent form of complex...
Article
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In previously identified forms of remote synchronization between two nodes, the intermediate portion of the network connecting the two nodes is not synchronized with them but generally exhibits some coherent dynamics. Here we report on a network phenomenon we call incoherence-mediated remote synchronization (IMRS), in which two non-contiguous parts...
Article
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In a network, a local disturbance can propagate and eventually cause a substantial part of the system to fail in cascade events that are easy to conceptualize but extraordinarily difficult to predict. Here, we develop a statistical framework that can predict cascade size distributions by incorporating two ingredients only: the vulnerability of indi...
Article
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The relation between network structure and dynamics is determinant for the behavior of complex systems in numerous domains. An important longstanding problem concerns the properties of the networks that optimize the dynamics with respect to a given performance measure. Here we show that such optimization can lead to sensitive dependence of the dyna...
Article
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Spontaneous synchronization has long served as a paradigm for behavioral uniformity that can emerge from interactions in complex systems. When the interacting entities are identical and their coupling patterns are also identical, the complete synchronization of the entire network is the state inheriting the system symmetry. As in other systems subj...
Article
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Synchronization in networks of coupled oscillators is known to be largely determined by the spectral and symmetry properties of the interaction network. Here, we leverage this relation to study a class of networks for which the threshold coupling strength for global synchronization is the lowest among all networks with the same number of nodes and...
Conference Paper
Full-text available
Frequency synchronization of power generators is a necessary condition for the operation of power-grid networks. The robustness of synchronous states to disturbances can be quantified in terms of their stability Here, applying a combination of perturbative analysis and numerical optimization techniques, we explore the landscape of synchronization s...
Article
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The dynamics of power-grid networks is becoming an increasingly active area of research within the physics and network science communities. The results from such studies are typically insightful and illustrative, but are often based on simplifying assumptions that can be either difficult to assess or not fully justified for realistic applications....
Article
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Slow parameter drift is common in many systems (e.g., the amount of greenhouse gases in the terrestrial atmosphere is increasing). In such situations, the attractor on which the system trajectory lies can be destroyed, and the trajectory will then go to another attractor of the system. We consider the case where there are more than one of these pos...
Article
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The metabolic network of a living cell involves several hundreds or thousands of interconnected biochemical reactions. Previous research has shown that under realistic conditions only a fraction of these reactions is concurrently active in any given cell. This is partially determined by nutrient availability, but is also strongly dependent on the m...
Data
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Supplementary Information
Article
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The study of collective dynamics in complex networks has emerged as a next frontier in the science of networks. This Focus Issue presents the latest developments on this exciting front, focusing in particular on synchronous and cascading dynamics, which are ubiquitous forms of network dynamics found in a wide range of physical, biological, social,...
Article
Model reduction is a common goal in the study of complex systems, consisting of many components with a complex interaction structure. The quality of such reduction, however, may not be reflected correctly in the stepwise prediction error in the model since it ignores the global geometry of the dynamics. Here we introduce a general two-step framewor...
Article
Given the abundance of relational data from a variety of sources, it is becoming increasingly more important to be able to discover hidden structures in the topology of real-world complex networks. In this talk, I will extend the usual definition of groups as densely connected sets of nodes and show that many real networks have groups distinguished...
Article
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Determining the effect of structural perturbations on the eigenvalue spectra of networks is an important problem because the spectra characterize not only their topological structures, but also their dynamical behavior, such as synchronization and cascading processes on networks. Here we develop a theory for estimating the change of the largest eig...
Article
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A common goal in the study of high dimensional and complex system is to model the system by a low order representation. In this letter we propose a general approach for assessing the quality of a reduced order model for high dimensional chaotic systems. The key of this approach is the use of optimal shadowing, combined with dimensionality reduction...
Article
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We derive a master stability function (MSF) for synchronization in networks of coupled dynamical systems with small but arbitrary parametric variations. Analogous to the MSF for identical systems, our generalized MSF simultaneously solves the linear-stability problem for near-synchronous states (NSS) for all possible connectivity structures. We als...
Article
In a network of dynamical elements, one of the most fundamental issues is the relationship between the network structure and the collective dynamics of the system. The study of complete synchronization, a simplest form of collective dynamics in a network, in which all oscillators behave in precisely the same way, provides an excellent starting poin...
Article
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Metabolic reactions of single-cell organisms are routinely observed to become dispensable or even incapable of carrying activity under certain circumstances. Yet, the mechanisms as well as the range of conditions and phenotypes associated with this behavior remain very poorly understood. Here we predict computationally and analytically that any org...
Data
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Mathematical Results (0.06 MB PDF)
Conference Paper
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We derive variational equations to analyze the stability of synchronization for coupled near-identical oscillators. To study the effect of parameter mismatch on the stability in a general fashion, we define master stability equations and associated master stability functions, which are independent of the network structure. In particular, we present...
Article
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We study a class of networks generated by sequences of letters taken from a finite alphabet consisting of m letters (corresponding to m types of nodes) and a fixed set of connectivity rules. Recently, it was shown how a binary alphabet might generate threshold nets in a similar fashion [A. Hagberg, Phys. Rev. E 74, 056116 (2006)]. Just like thresho...
Article
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Full understanding of synchronous behavior in coupled dynamical systems beyond the identical case requires an explicit construction of the generalized synchronization manifold, whether we wish to compare the systems, or to understand their stability. Nonetheless, while synchronization has become an extremely popular topic, the bulk of the research...
Article
Single-cell organisms are assumed to optimize growth under specific conditions. Using flux balance analysis, it is possible to estimate the number of reactions that are utilized (active) by the metabolism in random and optimal metabolic states. Here we investigate the mechanisms that determine the number of active reactions mathematically and compa...
Article
We consider two optimization problems on synchronization of oscillator networks: maximization of synchronizability and minimization of synchronization cost. We first develop an extension of the well-known master stability framework to the case of non-diagonalizable Laplacian matrices. We then show that the solution sets of the two optimization prob...
Article
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We consider maximization of the synchronizability of oscillator networks by assigning weights and directions to the links of a given interaction topology. By extending the master stability formalism to all possible network structures, we show that, unless some oscillator is linked to all the others, maximally synchronizable networks are necessarily...
Article
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We consider the problem of maximizing the synchronizability of oscillator networks by assigning weights and directions to the links of a given interaction topology. We first extend the well-known master stability formalism to the case of non-diagonalizable networks. We then show that, unless some oscillator is connected to all the others, networks...
Article
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This paper presents a perspective in the study of complex networks by focusing on how dynamics may affect network security under attacks. In particular, we review two related problems: attack-induced cascading breakdown and range-based attacks on links. A cascade in a network means the failure of a substantial fraction of the entire network in a ca...
Article
Inspired by the discovery of possible roles of synchronization of oscillations in the brain, networks of coupled phase oscillators have been proposed before as models of associative memory based on the concept of temporal coding of information. Here we show, however, that error-free retrieval states of such networks turn out to be typically unstabl...
Chapter
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This paper reviews two problems in the security of complex networks: cascades of overload failures on nodes and range-based attacks on links. Cascading failures have been reported for numerous networks and refer to the subsequent failure of other parts of the network induced by the failure of or attacks on only a few nodes. We investigate a mechani...
Article
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Networks of coupled periodic oscillators (similar to the Kuramoto model) have been proposed as models of associative memory. However, error-free retrieval states of such oscillatory networks are typically unstable, resulting in a near zero capacity. This puts the networks at disadvantage as compared with the classical Hopfield network. Here we prop...
Article
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Many examples of chemical and biological processes take place in large-scale environmental flows. Such flows generate filamental patterns which are often fractal due to the presence of chaos in the underlying advection dynamics. In such processes, hydrodynamical stirring strongly couples into the reactivity of the advected species and might thus ma...
Article
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The characterization of large-scale structural organization of social networks is an important interdisciplinary problem. We show, by using scaling analysis and numerical computation, that the following factors are relevant for models of social networks: the correlation between friendship ties among people and the position of their social groups, a...
Article
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Small-world and scale-free networks are known to be more easily synchronized than regular lattices, which is usually attributed to the smaller network distance between oscillators. Surprisingly, we find that networks with a homogeneous distribution of connectivity are more synchronizable than heterogeneous ones, even though the average network dist...
Article
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We consider a system of N phase oscillators having randomly distributed natural frequencies and diagonalizable interactions among the oscillators. We show that in the limit of N going to infinity, all solutions of such a system are incoherent with probability one for any strength of coupling, which implies that there is no sharp transition from inc...
Article
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The small-world phenomenon in complex networks has been identified as being due to the presence of long-range links, i.e., links connecting nodes that would otherwise be separated by a long node-to-node distance. We find, surprisingly, that many scale-free networks are more sensitive to attacks on short-range than on long-range links. This result,...
Article
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Efficiency in passage times is an important issue in designing networks, such as transportation or computer networks. The small-world networks have structures that yield high efficiency, while keeping the network highly clustered. We show that among all networks with the small-world structure, the most efficient ones have a "single center" node, fr...
Article
We investigate the effect of asynchronism of autocatalytic reactions taking place in open hydrodynamical flows, by assigning a phase to each particle in the system to differentiate the timing of the reaction, while the reaction rate (periodicity) is kept unchanged. The chaotic saddle in the flow dynamics acts as a catalyst and enhances the reaction...
Article
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A small (but finite-size) spherical particle advected by fluid flows obeys equations of motion that are inherently dissipative, due to the Stokes drag. The dynamics of the advected particle can be chaotic even with a flow field that is simply time periodic. Similar to the case of ideal tracers, whose dynamics is Hamiltonian, chemical or biological...
Article
We investigate the reaction kinetics of small spherical particles with inertia, obeying coalescence type of reaction, B+B-->B, and being advected by hydrodynamical flows with time-periodic forcing. In contrast to passive tracers, the particle dynamics is governed by the strongly nonlinear Maxey-Riley equations, which typically create chaos in the s...
Article
. We prove that the function from an invariant set of a typical dynamical system into R d , dened by successive inter-event time intervals from integrate-and-re dynamics, is prevalently a topological embedding. This allows topological information about a dynamical attractor to be inferred from spike trains. 1. Introduction In this paper we will pre...
Article
This thesis contains two separate topics. The first topic concerns proof of a theorem that justifies the method of reconstruction of dynamics using inter-event time intervals. In particular, we prove that the function from an invariant set of a typical dynamical system into R d, defined by successive inter-event time intervals from integrate-and-fi...
Article
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We analyze a class of piecewise linear parabolic maps on the torus, namely those obtained by considering a linear map with double eigenvalue one and taking modulo one in each component. We show that within this two parameter family of maps, the set of noninvertible maps is open and dense. For cases where the entries in the matrix are rational we sh...