Complex and Adaptive Dynamical Systems: A Primer
by Claudius Gros
Publisher: arXiv 2008
Number of pages: 276
This textbook covers a wide range of concepts, notions and phenomena of a truly interdisciplinary subject of rapidly growing importance. Complex system theory deals with dynamical systems containing a very large number of variables, showing a plethora of emergent features, arising in a broad range of contexts.
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by Valerio Lucarini, et al. - arXiv
This book provides a comprehensive introduction for the study of extreme events in the context of dynamical systems. It provides an overview of the area, underlining its relevance for mathematics, natural sciences, engineering, and social sciences.
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The goal of these notes is to give a reasonably complete, although not exhaustive, discussion of what is commonly referred to as the Hopf bifurcation with applications to specific problems, including stability calculations.
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With a good background in nonlinear dynamics, chaos theory, and applications, the authors give a treatment of the basic principles of nonlinear dynamics in different fields. In addition, they show overlap with the traditional field of control theory.
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This article will take up the question of what underlies the quantum formalism, whether it can be derived from simpler mathematical structures, and if so, what physical properties a system must possess in order for the formalism to hold.