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Introduction
The topic of this book is the stability analysis of continuous finite dimensional systems. The book consists of 13 chapters and two appendices.
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10. Aizerman’s Problem for Nonautonomous Systems
Let b k (t) (t≥ 0; k=1, ... , n) be real non-negative scalar-valued functions having continuous derivatives up to...
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Desynchronization and Chaos in the Kuramoto Model
Abstract. The Kuramoto model of N globally coupled phase oscillators is an essentially non-linear dynamical system with a rich dynamical behavior and...
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Spatially Extended Monotone Map**s
This chapter deals with the study of travelling waves in discrete time spatially extended systems with monotone dynamics. Such systems appear for...
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Optimal Control of Stochastic Processes
Many control problems appearing for complex systems are subject to imperfectly known disturbances. As we have learned in the previous chapter, these...
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Applications of the Correlation Length
The correlation length is the system–dependent parameter, which defines the structure of the dominant current–carrying (electric or fluid) paths....
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Pressure Saturation Curves and the Critical Volume Fraction for Percolation
The pressure-saturation curves of porous media give fundamental information about the pore space. In equilibrium, ignoring effects due to hysteresis,...
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Effects of Multi-Scale Heterogeneity
It is generally agreed that problems with multi-scale heterogeneity present the biggest challenge to computation and understanding. A few such...
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From Classical Connectionist Models to Probabilistic/Generalised Regression Neural Networks (PNNs/GRNNs)
This chapter begins by briefly summarising some of the well-known classical connectionist/artificial neural network models such as multi-layered...
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Language and Thinking Modules
In this chapter, we focus upon the two modules which are closely tied to the concept of “action planning”, i.e. the 1) language and 2) thinking...
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Sensation and Perception Modules
In any kind of creature, both the mechanisms of sensation and perception are indispensable for continuous living, e.g. to find edible plants/fruits...
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12. Orbital Stability and Forced Oscillations
Let us consider a system described by the equation...
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1. Preliminaries
In the sequel, C n is an n-dimensional complex Euclidean space and...
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The CML2004 Project
Coupled map lattices (CML) are basic models for the time evolution of nonlinear systems which, above all, are extended in space or involve many...
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The Frenkel–Kontorova Model
In the preface to his monograph on the structure of Evolutionary Theory [1], the late professor Stephen Jay Gould attributes to the philosopher...
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On Phase Transitions in Coupled Map Lattices
Coupled map lattices are a paradigm for studying fundamental questions in spatially extended dynamical systems. Within this tutorial we focus on...
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6 Fundamental “Uncertainty” in Science
The conference on “Uncertainty and Surprise” was concerned with our fundamental inability to predict future events. How can we restructure...
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17 Uncertainty as Certaint
I am trying to make money in the biotech industry from complexity science. And I am doing it with inspiration that I picked up on the edge of...
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2 Surprises in a Half Century
Ilya Prigogine participated early in the organization of our meeting and was invited to give a keynote address. Due to poor health he...
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9 A View from the Inside: The Task of Managing Uncertainty and Surprise
Let me shift the flow of the day a little bit, because I am not here to present a theory, or prove a theory. Actually, I come here with questions....