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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Journal ArticleDOI
Chaos in GDP
TL;DR: In this article, a nonlinear lower-dimensional discrete dynamic macroeconomic model is proposed to characterize GDP and the model is represented by a set of differential equations, and the analysis is performed using Mathematica and MS Excel programs.
Journal ArticleDOI
Complex response to periodic inhibition in simple and detailed neuronal models
TL;DR: It is found that only the biophysical model with voltage-sensitive conductances can produce chaotic behavior in a leaky integrate-and-fire neural model of the rat neuron.
Journal Article
Teaching Reaction Engineering Using the Attainable Region
Matthew J. Metzger,Matthew J. Metzger,Benjamin J. Glasser,David Glasser,Brendon Hausberger,Diane Hildebrandt +5 more
TL;DR: In this paper, the degree of mixing achieved of a PFR is compared to the PFR of the next PFR in terms of the number of PFRs in the reaction network.
Dissertation
Semiclassics beyond the diagonal approximation
TL;DR: In this article, the spectral properties of chaotic closed quantum systems are studied and the authors show that the spectral statistics of chaotic systems are universal and can be described by random-matrix theory.
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Computer simulations, exact trajectories, and the gravitational N-body problem
TL;DR: In this paper, a shadow is defined as an exact trajectory of a chaotic map or ordinary differential equation that remains close to an approximate solution for a nontrivial duration of time.
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.