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1. Introduction

   Nonlinear systems model all but the simplest physical phenomena. In the classical theory, the tools of Poisson geometry appear in an essential way,...

   The Editors in Integrability of Nonlinear Systems

   Chapter
   

2. Critical Phenomena in a Small World

   We consider the behavior of various systems on a small-world network near a critical point. Our starting point is a different, nonrandom system with...

   Matthew B. Hastings, Balázs Kozma in Complex Networks

   Chapter
   

3. Who Is the Best Connected Scientist?A Study of Scientific Coauthorship Networks

   Using data from computer databases of scientific papers in physics, biomedical research, and computer science, we have constructed networks of...

   Mark E.J. Newman in Complex Networks

   Chapter
   

4. Scholarly Information Network

   I review the background and some recent trends of a particular scholarly information network, ar**v.org, and discuss some of its implications for new...

   Paul Ginsparg in Complex Networks

   Chapter
   

5. Spectral Analysis of Random Networks

   We review a general approach that describes the spectra of eigenvalues for random graphs with a local tree-like structure. The exact equations to the...

   Sergei N. Dorogovtsev, Alexander V. Goltsev, ... Alexander N. Samukhin in Complex Networks

   Chapter
   

6. Theoretical Neuroanatomy:Analyzing the Structure, Dynamics,and Function of Neuronal Networks

   The mammalian brain is an extraordinary object: its networks give rise to our conscious experiences as well as to the generation of adaptive behavior...

   Anil K. Seth, Gerald M. Edelman in Complex Networks

   Chapter
   

7. Information Theory of Complex Networks: On Evolution and Architectural Constraints

   Complex networks are characterized by highly heterogeneous distributions of links, often pervading the presence of key properties such as robustness...

   Ricard V. Solé, Sergi Valverde in Complex Networks

   Chapter
   

8. Distance to Bifurcation in Multidimensional Parameter Space: Margin Sensitivity and Closest Bifurcations

   The problem of operating or designing a system with robust stability with respect to many parameters can be viewed as a geometric problem in...

   Ian Dobson in Bifurcation Control

   Chapter
   

9. Parameter Identifiability of Nonlinear Biological Systems

   Parameters characterizing the internal behaviour of biological and physiological systems are usually not directly accessible to measurement. Their...

   Mariapia Saccomani, Stefania Audoly, ... Leontina D’Angiò in Positive Systems

   Conference paper
   

10. Qualitative Analysis of Regulatory Graphs: A Computational Tool Based on a Discrete Formal Framework

    Building upon the logical approach developed by the group of R. Thomas in Brussels, we are defining a rigorous mathematical framework to model...

    Claudine Chaouiya, Elisabeth Remy, ... Denis Thieffry in Positive Systems

    Conference paper
    

11. Differential Systems with Positive Variables

    The variables of biological, ecological, or chemical systems are often positive, because they measure concentrations, numbers, ...We study polynomial...

    Jean-Luc Gouzé in Positive Systems

    Conference paper
    

12. Completion Problems for Positive Matrices with Minimal Rank

    Matrix completion problems studies the partial matrices, that is, a rectangular matrix some of whose entries are specified, and the remainder entries...

    Rafael Cantó, Ana M. Urbano in Positive Systems

    Conference paper
    

13. Linear Positive Systems and Phase-type Representations

    In this paper we try to put a bridge between the theory of phase-type distributions and the general theory of positive linear systems. The phase-type...

    Christian Commault in Positive Systems

    Conference paper
    

14. Estimation and Strong Approximation of Hidden Markov Models

    We give novel conditions for the existence of the limit of the normalized log-likelihood function for a finite-state continuous read-out Hidden...

    László Gerencsér, Gábor Molnár-Sáska in Positive Systems

    Conference paper
    

15. Modal Logic and Dioids

    This paper presents results concerning the relations between a propositional modal logic (NK-logic) and the algebra of dioids. The technique of...

    Christiano P. Pessanha, Rafael Santos-Mendes in Positive Systems

    Conference paper
    

16. Chaos and Pseudo-Randomness

    We discuss the effect on finite machine implementation of chaotic system on randomness. We show that the most significant bit even for fully...

    Ljupco Kocarev, Goce Jakimoski, Zarko Tasev in Chaos Control

    Chapter
    

17. Formation Mechanisms and Control Methods of Beam Halo-Chaos in High-Current Ion Linacs

    This chapter introduces some potential applications of ion beam in high-current ion linacs, and discusses two key issues in such applications...

    **-Qing Fang, Guanrong Chen, **nghuo Yu in Chaos Control

    Chapter
    

18. Bifurcation Analysis with Application to Power Electronics

    The problem of sudden loss of stability (more precisely, sudden change of operating behaviour) is frequently encountered in power electronics. A...

    Chi K. Tse, Octavian Dranga in Bifurcation Control

    Chapter
    

19. Local Robustness of Bifurcation Stabilization with Applications to Jet Engine Control

    Local robustness of bifurcation stabilization is studied for parameterized nonlinear systems of which the linearized system possesses either a simple...

    **ang Chen, Ali Tahmasebi, Guoxiang Gu in Bifurcation Control

    Chapter
    

20. Static Bifurcation in Mechanical Control Systems

    Feedback regulation of nonlinear dynamical systems inevitably leads to issues concerning static bifurcation. Static bifurcation in feedback systems...

    Harry G. Kwatny, Bor-Chin Chang, Shiu-** Wang in Bifurcation Control

    Chapter