Open AccessBook
Chaos: An Introduction to Dynamical Systems
TLDR
One-dimensional maps, two-dimensional map, fractals, and chaotic attraction attractors have been studied in this article for state reconstruction from data, including the state of Washington.Abstract:
One-Dimensional Maps.- Two-Dimensional Maps.- Chaos.- Fractals.- Chaos in Two-Dimensional Maps.- Chaotic Attractors.- Differential Equations.- Periodic Orbits and Limit Sets.- Chaos in Differential Equations.- Stable Manifolds and Crises.- Bifurcations.- Cascades.- State Reconstruction from Data.read more
Citations
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Persistent topological features of dynamical systems
TL;DR: The method presented here may be used as a generic method for constructing simplicial complex from a scalar time series that has a number of advantages compared to the mapping of the same time series to a complex network.
Journal ArticleDOI
Periodic Orbits in a Class of Re-Entrant Manufacturing Systems
TL;DR: It is proved that these vector fields show only periodic or eventually periodic orbits and an algorithm to determine the period of the orbits is presented.
Epidemic Spreading in Technological Networks
TL;DR: A new epidemiological model is proposed to account for particular characteristics of computer worm epidemics, which incorporates new aspects related to the availability of antivirus signatures, to the existence of direct immunization, and to the presence of a curing phase.
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The dynamics of the best individuals in co-evolution
Elena Popovici,Kenneth de Jong +1 more
TL;DR: This work has constructed a methodology for analyzing co-evolutionary dynamics based on trajectories of best-of-generation individuals and applied this methodology to gain insights into how to tune certain algorithm parameters in order to improve performance.
References
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Journal ArticleDOI
Synchronization in chaotic systems
TL;DR: This chapter describes the linking of two chaotic systems with a common signal or signals and highlights that when the signs of the Lyapunov exponents for the subsystems are all negative the systems are synchronized.
Journal ArticleDOI
The Fractal Geometry of Nature
TL;DR: A blend of erudition (fascinating and sometimes obscure historical minutiae abound), popularization (mathematical rigor is relegated to appendices) and exposition (the reader need have little knowledge of the fields involved) is presented in this article.
Book
Theory of Ordinary Differential Equations
TL;DR: The prerequisite for the study of this book is a knowledge of matrices and the essentials of functions of a complex variable as discussed by the authors, which is a useful text in the application of differential equations as well as for the pure mathematician.