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
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Storage and the Volatility of Agricultural Prices: A Model of Endogenous Fluctuations
Sophie Mitra,Jean-Marc Boussard +1 more
TL;DR: In this paper, a nonlinear Cobweb model with endogenous volatility was developed to identify the sources of food price volatility, which accounts for several characteristics of agricultural commodity markets and leads to price series with positive skewness and auto-correlation.
Posted Content
Expected Utility in Models with Chaos
TL;DR: In this paper, the authors provide a framework for calculating expected utility in models with chaotic equilibria and consequently a ranking framework for ranking chaos, where a dynamical system f : X! X where X is a compact metric space and f is continuous.
Journal ArticleDOI
On the dynamics of a periodic Colpitts oscillator forced by periodic and chaotic signals
TL;DR: The chaos produced in the slave Colpitts oscillator for a chaotic forcing is found to be in a phase-synchronized state with the forced chaos for some values of the coupling factor.
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Stabilization of periodic orbits of discrete-time dynamical systems using the Prediction-Based Control: New control law and practical aspects
Thiago Pereira das Chagas,Pierre-Alexandre Bliman,Pierre-Alexandre Bliman,Karl Heinz Kienitz +3 more
TL;DR: A new control law is proposed for the stabilization of periodic orbits of nonlinear discrete-time dynamical systems with chaotic sets, which sets all the Floquet multipliers of the stabilized orbit to zero, resulting in fast convergence of trajectories in its vicinity.
Analysis, Control and Synchronization of nonlinear systems and networks via Contraction Theory: theory and applications
TL;DR: The aim of the Thesis is providing a coherent theoretical framework for the study of networked systems, modeled by means of Ordinary Differential Equations with applications to biochemical networks, based on the use of a generalized version of contraction theory.
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.