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Orbit Dynamics, Stability and Chaos in Planetary Systems
Let us start with a problem of dynamical biology, which was posed about 800 years ago by Fibonacci1 -
Coupled Map Lattices: at the Age of Maturity
Coupled Map Lattices (CML) were simultaneously and independently introduced by K. Kaneko, R. Kapral and S. Kuznetsov in 1983–84 [1, 2, 3, 4, 5, 6].... -
Deterministic Control Theory
In this chapter we focus our attention on the open loop control of deterministic problems. We will see that the language of deterministic control... -
Optimization Problems
Several problems, for example Pontryagin’s maximum principle or the minimax problems of game theoretical approaches, require the determination of an... -
Aerothermodynamics, Nonlinear Acoustics and the Meteorological Equations
The study of low-Mach-number flows occurs in the general context of asymptotic modelling of fluid flows, and in a recent book (Zeytounian 2004, Chap.... -
Planet Formation
Motivating the study of planet formation is not difficult for any curious audience. One of the fundamental human questions is that of origins: “where... -
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... -
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... -
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... -
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... -
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... -
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... -
Some Aspects of Low-Mach-Number External Flows
In this chapter, we consider first, in Sect. 4.1, a detailed derivation of the Navier–Fourier initial–boundary–value problem for the Navier velocity... -
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... -
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... -
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... -
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.... -
4 The Evolutionary Complexity of Social Economic Systems: The Inevitability of Uncertainty and Surprise
In order to improve our quality of life and the successful functioning of our organisations and social institutions, or to mitigate some anticipated... -
7 The Complementary Nature of Coordination Dynamics: Toward a Science of the In-Between
My take-off point in this brief essay is the following comment from the introductory material that all the participants received for the conference... -
1 Uncertainty and Surprise: An Introduction
Much of the traditional scientific and applied scientific work in the social and natural sciences has been built on the supposition that the...