Steven H. Strogatz

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.

Predicted power laws for delayed switching of charge-density waves

Abstract: Etude de 3 modeles dont chacun predit une dependance en forme de loi puissance du retard de commutation pres du seuil vis-a-vis de la distance normalisee au-dela du champ seuil. On presente les divergences entre les modeles de Hall et Mihaly d'une part et Strogatz d'autre part, en employant la theorie de la bifurcation. Ces differences permettent de distinguer les modeles experimentalement

The Birth of Period Three

Abstract: Xn+l = rXnO -Xn),(1) where 0 < x_ 1 and 0 < r < 4. In other words, given some starting number 0 < xl < 1, we generate a new number x2 by the rule x2 = rx1(1 x 1), and then repeat the process to generate x3 from x2, and so on. This equation has many virtues: 1) It is accessible. High school students can explore its patterns, as long as they have access to a hand calculator or a small computer. 2) It is exemplary. This single example illustrates many of the fundamental notions of nonlinear dynamics, such as equilibrium, stability, periodicity, chaos, bifurcations, and fractals. May [6] was the first to stress the pedagogical value of (1). 3) It is living mathematics. Most of the important discoveries about the logistic map are less than 20 years old. Certain aspects of (1) are still not understood rigorously, and are being pursued by a few of the finest living mathematicians. 4) It is relevant to science. Predictions derived from the logistic map have been verified in experiments on weakly turbulent fluids, oscillating chemical reactions, nonlinear electronic circuits, and a variety of other systems [8].

Scaling laws for dynamical hysteresis in a multidimensional laser system.

Abstract: We examine scaling laws for dynamical hysteresis in an optically bistable semiconductor laser. An analytic derivation of these laws from multidimensional laser equations is outlined and they are expected to be universal for systems that exhibit a cusp catastrophe. The scaling laws for the hysteresis loop area or width are numerically verified and experimentally measured for operation of the bistable laser above and below threshold. Excellent agreement with theory is obtained in the limit of low switching frequencies.

Nonlinear dynamics of a solid-state laser with injection

Abstract: We analyze the dynamics of a solid-state laser driven by an injected sinusoidal field. For this type of laser, the cavity round-trip time is much shorter than its fluorescence time, yielding a dimensionless ratio of time scales $\ensuremath{\sigma}\ensuremath{\ll}1.$ Analytical criteria are derived for the existence, stability, and bifurcations of phase-locked states. We find three distinct unlocking mechanisms. First, if the dimensionless detuning \ensuremath{\Delta} and injection strength $k$ are small in the sense that $k=O(\ensuremath{\Delta})\ensuremath{\ll}{\ensuremath{\sigma}}^{1/2},$ unlocking occurs by a saddle-node infinite-period bifurcation. This is the classic unlocking mechanism governed by the Adler equation: after unlocking occurs, the phases of the drive and the laser drift apart monotonically. The second mechanism occurs if the detuning and the drive strength are large: $k=O(\ensuremath{\Delta})\ensuremath{\gg}{\ensuremath{\sigma}}^{1/2}.$ In this regime, unlocking is caused instead by a supercritical Hopf bifurcation, leading first to phase trapping and only then to phase drift as the drive is decreased. The third and most interesting mechanism occurs in the distinguished intermediate regime $k,$ $\ensuremath{\Delta}=O({\ensuremath{\sigma}}^{1/2}).$ Here the system exhibits complicated, but nonchaotic, behavior. Furthermore, as the drive decreases below the unlocking threshold, numerical simulations predict a self-similar sequence of bifurcations, the details of which are not yet understood.

Education of a model student.

Abstract: A dilemma faced by teachers, and increasingly by designers of educational software, is the trade-off between teaching new material and reviewing what has already been taught. Complicating matters, review is useful only if it is neither too soon nor too late. Moreover, different students need to review at different rates. We present a mathematical model that captures these issues in idealized form. The student’s needs are modeled as constraints on the schedule according to which educational material and review are spaced over time. Our results include algorithms to construct schedules that adhere to various spacing constraints, and bounds on the rate at which new material can be introduced under these schedules.

Collective dynamics of small-world networks

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.

Emergence of Scaling in Random Networks

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.

疟原虫var基因转换速率变化导致抗原变异[英]／Paul H, Robert P, Christodoulou Z, et al//Proc Natl Acad Sci U S A

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。

Statistical mechanics of complex networks

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.

The Structure and Function of Complex 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.