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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
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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]....
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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...
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Optimization Problems
Several problems, for example Pontryagin’s maximum principle or the minimax problems of game theoretical approaches, require the determination of an...
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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...
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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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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....
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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...
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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...
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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...
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Method of Invariant Grids
The method of invariant grids is developed for a grid-based computation of invariant manifolds.
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Invariance Equation in Differential Form
Definition of invariance in terms of motions and trajectories assumes, at least, existence and uniqueness theorems for solutions of the original...