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Author

Renato Spigler

Other affiliations: Sapienza University of Rome, New York University, Leonardo  ...read more
Bio: Renato Spigler is an academic researcher from Roma Tre University. The author has contributed to research in topics: Nonlinear system & Differential equation. The author has an hindex of 23, co-authored 150 publications receiving 4283 citations. Previous affiliations of Renato Spigler include Sapienza University of Rome & New York University.


Papers
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Journal ArticleDOI
TL;DR: In this paper, a review of the Kuramoto model of coupled phase oscillators is presented, with a rigorous mathematical treatment, specific numerical methods, and many variations and extensions of the original model that have appeared in the last few years.
Abstract: Synchronization phenomena in large populations of interacting elements are the subject of intense research efforts in physical, biological, chemical, and social systems. A successful approach to the problem of synchronization consists of modeling each member of the population as a phase oscillator. In this review, synchronization is analyzed in one of the most representative models of coupled phase oscillators, the Kuramoto model. A rigorous mathematical treatment, specific numerical methods, and many variations and extensions of the original model that have appeared in the last few years are presented. Relevant applications of the model in different contexts are also included.

2,864 citations

Journal ArticleDOI
TL;DR: In this paper, a mean field model of nonlinearly coupled oscillators with randomly distributed frequencies and subject to independent external white noises is analyzed in the thermodynamic limit, and new results include subcritical spontaneous stationary synchronization of the oscillators, supercritical time-periodic synchronization, bistability and hysteretic phenomena.
Abstract: A mean-field model of nonlinearly coupled oscillators with randomly distributed frequencies and subject to independent external white noises is analyzed in the thermodynamic limit. When the frequency distribution isbimodal, new results include subcritical spontaneous stationary synchronization of the oscillators, supercritical time-periodic synchronization, bistability, and hysteretic phenomena. Bifurcating synchronized states are asymptotically constructed near bifurcation values of the coupling strength, and theirnonlinear stability properties ascertained.

134 citations

Journal ArticleDOI
TL;DR: This paper studies pointwise and uniform convergence, as well as the order of approximation, for a family of linear positive neural network operators activated by certain sigmoidal functions, and shows that for C(1)-functions, the orders can be generalized to handle multivariate functions as well.

126 citations

Journal ArticleDOI
TL;DR: In this paper, a constructive theory for approximating func- tions of one or more variables by superposition of sigmoidal functions is developed, which is done in the uniform norm as well as in the L p norm.
Abstract: In this paper, a constructive theory is developed for approximating func- tions of one or more variables by superposition of sigmoidal functions. This is done in the uniform norm as well as in the L p norm. Results for the simultaneous approx- imation, with the same order of accuracy, of a function and its derivatives (whenever these exist), are obtained. The relation with neural networks and radial basis func- tions approximations is discussed. Numerical examples are given for the purpose of illustration.

95 citations

Journal ArticleDOI
TL;DR: In this paper, the mean field Kuramoto model describing the synchronization of a population of phase oscillators with a bimodal frequency distribution is analyzed near regions in its phase diagram corresponding to synchronization to phases with a time-periodic order parameter.

93 citations


Cited by
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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

Book ChapterDOI
01 Jan 2015

3,828 citations

Book
01 Oct 2006
TL;DR: This book explains the relationship of electrophysiology, nonlinear dynamics, and the computational properties of neurons, with each concept presented in terms of both neuroscience and mathematics and illustrated using geometrical intuition, providing a link between the two disciplines.
Abstract: This book explains the relationship of electrophysiology, nonlinear dynamics, and the computational properties of neurons, with each concept presented in terms of both neuroscience and mathematics and illustrated using geometrical intuition In order to model neuronal behavior or to interpret the results of modeling studies, neuroscientists must call upon methods of nonlinear dynamics This book offers an introduction to nonlinear dynamical systems theory for researchers and graduate students in neuroscience It also provides an overview of neuroscience for mathematicians who want to learn the basic facts of electrophysiology "Dynamical Systems in Neuroscience" presents a systematic study of the relationship of electrophysiology, nonlinear dynamics, and computational properties of neurons It emphasizes that information processing in the brain depends not only on the electrophysiological properties of neurons but also on their dynamical properties The book introduces dynamical systems starting with one- and two-dimensional Hodgkin-Huxley-type models and continuing to a description of bursting systems Each chapter proceeds from the simple to the complex, and provides sample problems at the end The book explains all necessary mathematical concepts using geometrical intuition; it includes many figures and few equations, making it especially suitable for non-mathematicians Each concept is presented in terms of both neuroscience and mathematics, providing a link between the two disciplines Nonlinear dynamical systems theory is at the core of computational neuroscience research, but it is not a standard part of the graduate neuroscience curriculum - or taught by math or physics department in a way that is suitable for students of biology This book offers neuroscience students and researchers a comprehensive account of concepts and methods increasingly used in computational neuroscience

3,683 citations

Journal ArticleDOI
TL;DR: Van Kampen as mentioned in this paper provides an extensive graduate-level introduction which is clear, cautious, interesting and readable, and could be expected to become an essential part of the library of every physical scientist concerned with problems involving fluctuations and stochastic processes.
Abstract: N G van Kampen 1981 Amsterdam: North-Holland xiv + 419 pp price Dfl 180 This is a book which, at a lower price, could be expected to become an essential part of the library of every physical scientist concerned with problems involving fluctuations and stochastic processes, as well as those who just enjoy a beautifully written book. It provides an extensive graduate-level introduction which is clear, cautious, interesting and readable.

3,647 citations

Journal ArticleDOI
TL;DR: In this paper, the authors describe the rules of the ring, the ring population, and the need to get off the ring in order to measure the movement of a cyclic clock.
Abstract: 1980 Preface * 1999 Preface * 1999 Acknowledgements * Introduction * 1 Circular Logic * 2 Phase Singularities (Screwy Results of Circular Logic) * 3 The Rules of the Ring * 4 Ring Populations * 5 Getting Off the Ring * 6 Attracting Cycles and Isochrons * 7 Measuring the Trajectories of a Circadian Clock * 8 Populations of Attractor Cycle Oscillators * 9 Excitable Kinetics and Excitable Media * 10 The Varieties of Phaseless Experience: In Which the Geometrical Orderliness of Rhythmic Organization Breaks Down in Diverse Ways * 11 The Firefly Machine 12 Energy Metabolism in Cells * 13 The Malonic Acid Reagent ('Sodium Geometrate') * 14 Electrical Rhythmicity and Excitability in Cell Membranes * 15 The Aggregation of Slime Mold Amoebae * 16 Numerical Organizing Centers * 17 Electrical Singular Filaments in the Heart Wall * 18 Pattern Formation in the Fungi * 19 Circadian Rhythms in General * 20 The Circadian Clocks of Insect Eclosion * 21 The Flower of Kalanchoe * 22 The Cell Mitotic Cycle * 23 The Female Cycle * References * Index of Names * Index of Subjects

3,424 citations