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Steven H. Strogatz

Other affiliations: Boston College, Purdue University, Boston University  ...read more
Bio: Steven H. Strogatz is an academic researcher from Cornell University. The author has contributed to research in topics: Kuramoto model & Josephson effect. The author has an hindex of 79, co-authored 219 publications receiving 85750 citations. Previous affiliations of Steven H. Strogatz include Boston College & Purdue University.


Papers
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Book
01 Jan 2003
TL;DR: 'SYNC' as mentioned in this paper is a story of a DAZZLING KIND OF ORDER in the universe, the HARMONY that COMES from cyclists in SYNC.
Abstract: 'SYNC' IS A STORY OF A DAZZLING KIND OF ORDER IN THE UNIVERSE, THE HARMONY THAT COMES FROM CYCLES IN SYNC. THE TENDENCY TO SYCHRONIZE IS ONE OF THE MOST FAR- REACHING DRIVES IN ALL OF NATURE. IT EXTENDS FROM PEOPLE TO PLANETS, FROM ANIMALS TO ATOMS. IN 'SYNC' PROFESSOR STEVEN STROGATZ CONSIDERS A RANGE OF APPLICATIONS - HUMAN SLEEP AND CIRCADIAN RHYTHMS, MENSTRUAL SYNCHRONY, INSECT OUTBREAKS, SUPERCONDUCTORS, LASERS, SECRET CODES, HEART ARRHYTHMIAS AND FADS - CONNECTING ALL TRHOUGH AN EXPLORATION OF THE SAME MATHEMATICAL THEME: SELF- ORGANISATION, OR THE SPONTANEOUS EMERGENCE OF ORDER OUT OF CHAOS. FOCUSED ENOUGH TO PRESENT A COHERENT WORLD UNTO THEMSELVES, STROGATZ'S CHOSEN TOPICS TOUCH ON SEVERAL OF THE HOTTEST DIRECTIONS IN CONTEMPORARY SCIENCE.

1,378 citations

Journal ArticleDOI
TL;DR: It is shown that the stable chimera state bifurcates from a spatially modulated drift state, and dies in a saddle-node biforcation with an unstable chimer state for a ring of phase oscillators coupled by a cosine kernel.
Abstract: Arrays of identical oscillators can display a remarkable spatiotemporal pattern in which phase-locked oscillators coexist with drifting ones. Discovered two years ago, such "chimera states" are believed to be impossible for locally or globally coupled systems; they are peculiar to the intermediate case of nonlocal coupling. Here we present an exact solution for this state, for a ring of phase oscillators coupled by a cosine kernel. We show that the stable chimera state bifurcates from a spatially modulated drift state, and dies in a saddle-node bifurcation with an unstable chimera state.

1,218 citations

Journal ArticleDOI
TL;DR: In this article, two possible approaches to secure communications are demonstrated with the Lorenz circuit implemented in both the transmitter and receiver, where a chaotic masking signal is added at the transmitter to the message, and at the receiver, the masking is regenerated and subtracted from the received signal.
Abstract: A circuit implementation of the chaotic Lorenz system is described. The chaotic behavior of the circuit closely matches the results predicted by numerical experiments. Using the concept of synchronized chaotic systems (SCS's), two possible approaches to secure communications are demonstrated with the Lorenz circuit implemented in both the transmitter and receiver. In the first approach, a chaotic masking signal is added at the transmitter to the message, and at the receiver, the masking is regenerated and subtracted from the received signal. The second approach utilizes modulation of the coefficients of the chaotic system in the transmitter and corresponding detection of synchronization error in the receiver to transmit binary-valued bit streams. The use of SCS's for communications relies on the robustness of the synchronization to perturbations in the drive signal. As a step toward further understanding the inherent robustness, we establish an analogy between synchronization in chaotic systems, nonlinear observers for deterministic systems, and state estimation in probabilistic systems. This analogy exists because SCS's can be viewed as performing the role of a nonlinear state space observer. To calibrate the robustness of the Lorenz SCS as a nonlinear state estimator, we compare the performance of the Lorenz SCS to an extended Kalman filter for providing state estimates when the measurement consists of a single noisy transmitter component. >

1,029 citations

Journal ArticleDOI
08 Aug 1986-Science
TL;DR: Exposure to bright light can indeed reset the human circadian pacemaker, which controls daily variations in physiologic, behavioral, and cognitive function, as indicated by recordings of body temperature and cortisol secretion.
Abstract: Human circadian rhythms were once thought to be insensitive to light, with synchronization to the 24-hour day accomplished either through social contacts or the sleep-wake schedule. Yet the demonstration of an intensity-dependent neuroendocrine response to bright light has led to renewed consideration of light as a possible synchronizer of the human circadian pacemaker. In a laboratory study, the output of the circadian pacemaker of an elderly woman was monitored before and after exposure to 4 hours of bright light for seven consecutive evenings, and before and after a control study in ordinary room light while her sleep-wake schedule and social contacts remained unchanged. The exposure to bright light in the evening induced a 6-hour delay shift of her circadian pacemaker, as indicated by recordings of body temperature and cortisol secretion. The unexpected magnitude, rapidity, and stability of the shift challenge existing concepts regarding circadian phase-resetting capacity in man and suggest that exposure to bright light can indeed reset the human circadian pacemaker, which controls daily variations in physiologic, behavioral, and cognitive function.

754 citations


Cited by
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Journal ArticleDOI
04 Jun 1998-Nature
TL;DR: Simple models of networks that can be tuned through this middle ground: regular networks ‘rewired’ to introduce increasing amounts of disorder are explored, finding that these systems can be highly clustered, like regular lattices, yet have small characteristic path lengths, like random graphs.
Abstract: Networks of coupled dynamical systems have been used to model biological oscillators, Josephson junction arrays, excitable media, neural networks, spatial games, genetic control networks and many other self-organizing systems. Ordinarily, the connection topology is assumed to be either completely regular or completely random. But many biological, technological and social networks lie somewhere between these two extremes. Here we explore simple models of networks that can be tuned through this middle ground: regular networks 'rewired' to introduce increasing amounts of disorder. We find that these systems can be highly clustered, like regular lattices, yet have small characteristic path lengths, like random graphs. We call them 'small-world' networks, by analogy with the small-world phenomenon (popularly known as six degrees of separation. The neural network of the worm Caenorhabditis elegans, the power grid of the western United States, and the collaboration graph of film actors are shown to be small-world networks. Models of dynamical systems with small-world coupling display enhanced signal-propagation speed, computational power, and synchronizability. In particular, infectious diseases spread more easily in small-world networks than in regular lattices.

39,297 citations

Journal ArticleDOI
15 Oct 1999-Science
TL;DR: A model based on these two ingredients reproduces the observed stationary scale-free distributions, which indicates that the development of large networks is governed by robust self-organizing phenomena that go beyond the particulars of the individual systems.
Abstract: Systems as diverse as genetic networks or the World Wide Web are best described as networks with complex topology. A common property of many large networks is that the vertex connectivities follow a scale-free power-law distribution. This feature was found to be a consequence of two generic mechanisms: (i) networks expand continuously by the addition of new vertices, and (ii) new vertices attach preferentially to sites that are already well connected. A model based on these two ingredients reproduces the observed stationary scale-free distributions, which indicates that the development of large networks is governed by robust self-organizing phenomena that go beyond the particulars of the individual systems.

33,771 citations

28 Jul 2005
TL;DR: PfPMP1)与感染红细胞、树突状组胞以及胎盘的单个或多个受体作用,在黏附及免疫逃避中起关键的作�ly.
Abstract: 抗原变异可使得多种致病微生物易于逃避宿主免疫应答。表达在感染红细胞表面的恶性疟原虫红细胞表面蛋白1(PfPMP1)与感染红细胞、内皮细胞、树突状细胞以及胎盘的单个或多个受体作用,在黏附及免疫逃避中起关键的作用。每个单倍体基因组var基因家族编码约60种成员,通过启动转录不同的var基因变异体为抗原变异提供了分子基础。

18,940 citations

Journal ArticleDOI
TL;DR: In this paper, a simple model based on the power-law degree distribution of real networks was proposed, which was able to reproduce the power law degree distribution in real networks and to capture the evolution of networks, not just their static topology.
Abstract: The emergence of order in natural systems is a constant source of inspiration for both physical and biological sciences. While the spatial order characterizing for example the crystals has been the basis of many advances in contemporary physics, most complex systems in nature do not offer such high degree of order. Many of these systems form complex networks whose nodes are the elements of the system and edges represent the interactions between them. Traditionally complex networks have been described by the random graph theory founded in 1959 by Paul Erdohs and Alfred Renyi. One of the defining features of random graphs is that they are statistically homogeneous, and their degree distribution (characterizing the spread in the number of edges starting from a node) is a Poisson distribution. In contrast, recent empirical studies, including the work of our group, indicate that the topology of real networks is much richer than that of random graphs. In particular, the degree distribution of real networks is a power-law, indicating a heterogeneous topology in which the majority of the nodes have a small degree, but there is a significant fraction of highly connected nodes that play an important role in the connectivity of the network. The scale-free topology of real networks has very important consequences on their functioning. For example, we have discovered that scale-free networks are extremely resilient to the random disruption of their nodes. On the other hand, the selective removal of the nodes with highest degree induces a rapid breakdown of the network to isolated subparts that cannot communicate with each other. The non-trivial scaling of the degree distribution of real networks is also an indication of their assembly and evolution. Indeed, our modeling studies have shown us that there are general principles governing the evolution of networks. Most networks start from a small seed and grow by the addition of new nodes which attach to the nodes already in the system. This process obeys preferential attachment: the new nodes are more likely to connect to nodes with already high degree. We have proposed a simple model based on these two principles wich was able to reproduce the power-law degree distribution of real networks. Perhaps even more importantly, this model paved the way to a new paradigm of network modeling, trying to capture the evolution of networks, not just their static topology.

18,415 citations

Journal ArticleDOI
TL;DR: Developments in this field are reviewed, including such concepts as the small-world effect, degree distributions, clustering, network correlations, random graph models, models of network growth and preferential attachment, and dynamical processes taking place on networks.
Abstract: Inspired by empirical studies of networked systems such as the Internet, social networks, and biological networks, researchers have in recent years developed a variety of techniques and models to help us understand or predict the behavior of these systems. Here we review developments in this field, including such concepts as the small-world effect, degree distributions, clustering, network correlations, random graph models, models of network growth and preferential attachment, and dynamical processes taking place on networks.

17,647 citations