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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Decentralized navigation method for a robotic swarm with nonhomogeneous abilities
TL;DR: With this method, the robotic swarm moves in a two-dimensional plane, and each follower distributedly constructs and maintains local directed connection using only local information to achieve maintenance of global connectivity.
Journal ArticleDOI
Electronically-implemented coupled logistic maps
TL;DR: This work design and characterize a simple, low-cost, easy-to-handle, electronic implementation of the logistic map, which allows for straightforward circuit-modifications to behave as different one-dimensional discrete-time systems.
Journal ArticleDOI
F-TRIDYN simulations of tungsten self-sputtering and applications to coupling plasma and material codes
Jon Drobny,Davide Curreli +1 more
TL;DR: Fractal-TRIDYN as discussed by the authors is an improved version of the Monte Carlo, Binary Collision Approximation code TRIDYN for simulating ion-surface interactions, which is also suited for the simulation of a wider range of plasma-surface interaction where surface morphology may play a role.
Proceedings ArticleDOI
Decentralized adaptive controller for synchronization of dynamical networks with delays and bounded disturbances
TL;DR: An adaptive master-slave output feedback synchronization problem is studied firstly for a network of interconnected nonlinear dynamical systems with bounded disturbance and then for anetwork of systems with delayed couplings, based on speed-gradient and passification methods.
Journal ArticleDOI
Characterization of the natural measure by unstable periodic orbits in nonhyperbolic chaotic systems
TL;DR: In this paper, the authors test the goodness of the unstable periodic-orbit characterization of the natural measure for non-hyperbolic chaotic systems and show that it is applicable to non-Hyperbolic systems.
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.