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Attractor Dimension Estimates for Dynamical Systems: Theory and Computation

2020-07-02 Computers
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Release : 2020-07-02
Genre : Computers
Kind : eBook
Book Rating : 877/5 ( reviews)

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Book Synopsis Attractor Dimension Estimates for Dynamical Systems: Theory and Computation by : Nikolay Kuznetsov

Download or read book Attractor Dimension Estimates for Dynamical Systems: Theory and Computation written by Nikolay Kuznetsov. This book was released on 2020-07-02. Available in PDF, EPUB and Kindle. Book excerpt: This book provides analytical and numerical methods for the estimation of dimension characteristics (Hausdorff, Fractal, Carathéodory dimensions) for attractors and invariant sets of dynamical systems and cocycles generated by smooth differential equations or maps in finite-dimensional Euclidean spaces or on manifolds. It also discusses stability investigations using estimates based on Lyapunov functions and adapted metrics. Moreover, it introduces various types of Lyapunov dimensions of dynamical systems with respect to an invariant set, based on local, global and uniform Lyapunov exponents, and derives analytical formulas for the Lyapunov dimension of the attractors of the Hénon and Lorenz systems. Lastly, the book presents estimates of the topological entropy for general dynamical systems in metric spaces and estimates of the topological dimension for orbit closures of almost periodic solutions to differential equations.

Chaotic Systems with Multistability and Hidden Attractors

2021-12-01 Technology & Engineering
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Release : 2021-12-01
Genre : Technology & Engineering
Kind : eBook
Book Rating : 214/5 ( reviews)

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Book Synopsis Chaotic Systems with Multistability and Hidden Attractors by : Xiong Wang

Download or read book Chaotic Systems with Multistability and Hidden Attractors written by Xiong Wang. This book was released on 2021-12-01. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a collection of new articles written by world-leading experts and active researchers to present their recent finding and progress in the new area of chaotic systems and dynamics, regarding emerging subjects of unconventional chaotic systems and their complex dynamics.It guide readers directly to the research front of the new scientific studies. This book is unique of its kind in the current literature, presenting broad scientific research topics including multistability and hidden attractors in unconventional chaotic systems, such as chaotic systems without equilibria, with only stable equilibria, with a curve or a surface of equilibria. The book describes many novel phenomena observed from chaotic systems, such as non-Shilnikov type chaos, coexistence of different types of attractors, and spontaneous symmetry breaking in chaotic systems. The book presents state-of-the-art scientific research progress in the field with both theoretical advances and potential applications. This book is suitable for all researchers and professionals in the areas of nonlinear dynamics and complex systems, including research professionals, physicists, applied mathematicians, computer scientists and, in particular, graduate students in related fields.

Artificial Intelligence Applications and Innovations

2021-06-22 Computers
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Release : 2021-06-22
Genre : Computers
Kind : eBook
Book Rating : 505/5 ( reviews)

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Book Synopsis Artificial Intelligence Applications and Innovations by : Ilias Maglogiannis

Download or read book Artificial Intelligence Applications and Innovations written by Ilias Maglogiannis. This book was released on 2021-06-22. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 17th IFIP WG 12.5 International Conference on Artificial Intelligence Applications and Innovations, AIAI 2021, held virtually and in Hersonissos, Crete, Greece, in June 2021. The 50 full papers and 11 short papers presented were carefully reviewed and selected from 113 submissions. They cover a broad range of topics related to technical, legal, and ethical aspects of artificial intelligence systems and their applications and are organized in the following sections: adaptive modeling/ neuroscience; AI in biomedical applications; AI impacts/ big data; automated machine learning; autonomous agents; clustering; convolutional NN; data mining/ word counts; deep learning; fuzzy modeling; hyperdimensional computing; Internet of Things/ Internet of energy; machine learning; multi-agent systems; natural language; recommendation systems; sentiment analysis; and smart blockchain applications/ cybersecurity. Chapter “Improving the Flexibility of Production Scheduling in Flat Steel Production Through Standard and AI-based Approaches: Challenges and Perspective” is available open access under a Creative Commons Attribution 4.0 International License via link.springer.com.

Attractors and Methods

2018-07-09 Mathematics
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Release : 2018-07-09
Genre : Mathematics
Kind : eBook
Book Rating : 084/5 ( reviews)

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Book Synopsis Attractors and Methods by : Boling Guo

Download or read book Attractors and Methods written by Boling Guo. This book was released on 2018-07-09. Available in PDF, EPUB and Kindle. Book excerpt: This two-volume work presents state-of-the-art mathematical theories and results on infinite-dimensional dynamical systems. Inertial manifolds, approximate inertial manifolds, discrete attractors and the dynamics of small dissipation are discussed in detail. The unique combination of mathematical rigor and physical background makes this work an essential reference for researchers and graduate students in applied mathematics and physics. The main emphasis in the fi rst volume is on the existence and properties for attractors and inertial manifolds. This volume highlights the use of modern analytical tools and methods such as the geometric measure method, center manifold theory in infinite dimensions, the Melnihov method, spectral analysis and so on for infinite-dimensional dynamical systems. The second volume includes the properties of global attractors, the calculation of discrete attractors, structures of small dissipative dynamical systems, and the existence and stability of solitary waves. Contents Discrete attractor and approximate calculation Some properties of global attractor Structures of small dissipative dynamical systems Existence and stability of solitary waves

Handbook of Dynamical Systems

2002-02-21 Science
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Release : 2002-02-21
Genre : Science
Kind : eBook
Book Rating : 845/5 ( reviews)

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Book Synopsis Handbook of Dynamical Systems by : B. Fiedler

Download or read book Handbook of Dynamical Systems written by B. Fiedler. This book was released on 2002-02-21. Available in PDF, EPUB and Kindle. Book excerpt: This handbook is volume II in a series collecting mathematical state-of-the-art surveys in the field of dynamical systems. Much of this field has developed from interactions with other areas of science, and this volume shows how concepts of dynamical systems further the understanding of mathematical issues that arise in applications. Although modeling issues are addressed, the central theme is the mathematically rigorous investigation of the resulting differential equations and their dynamic behavior. However, the authors and editors have made an effort to ensure readability on a non-technical level for mathematicians from other fields and for other scientists and engineers. The eighteen surveys collected here do not aspire to encyclopedic completeness, but present selected paradigms. The surveys are grouped into those emphasizing finite-dimensional methods, numerics, topological methods, and partial differential equations. Application areas include the dynamics of neural networks, fluid flows, nonlinear optics, and many others. While the survey articles can be read independently, they deeply share recurrent themes from dynamical systems. Attractors, bifurcations, center manifolds, dimension reduction, ergodicity, homoclinicity, hyperbolicity, invariant and inertial manifolds, normal forms, recurrence, shift dynamics, stability, to namejust a few, are ubiquitous dynamical concepts throughout the articles.

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