The first truly up-to-date look at the theory and capabilities of nonlinear dynamical systems that take the form of feedforward neural network structures Considered one of the most important types of structures in the study of neural networks and neural-like networks, feedforward networks incorporating dynamical elements have important properties and are of use in many applications. Specializing in experiential knowledge, a neural network stores and expands its knowledge base via strikingly human routes-through a learning process and information storage involving interconnection strengths known as synaptic weights. In Nonlinear Dynamical Systems: Feedforward Neural Network Perspectives, six leading authorities describe recent contributions to the development of an analytical basis for the understanding and use of nonlinear dynamical systems of the feedforward type, especially in the areas of control, signal processing, and time series analysis. Moving from an introductory discussion of the different aspects of feedforward neural networks, the book then addresses: * Classification problems and the related problem of approximating dynamic nonlinear input-output maps * The development of robust controllers and filters * The capability of neural networks to approximate functions and dynamic systems with respect to risk-sensitive error * Segmenting a time series It then sheds light on the application of feedforward neural networks to speech processing, summarizing speech-related techniques, and reviewing feedforward neural networks from the viewpoint of fundamental design issues. An up-to-date and authoritative look at the ever-widening technical boundaries and influence of neural networks in dynamical systems, this volume is an indispensable resource for researchers in neural networks and a reference staple for libraries.
The book is aimed at students and researchers in all the diverse fields in which nonlinear phenomena are important.
This book is an indispensable resource for applied mathematicians, dynamical systems theorists, control theorists, and engineers.
Then we have the following Morse lemma. Lemma 14.8.3 (Morse) If F is a Cr, r ≥ 3, or analytic Morse function near x = 0, then in a neighborhood of x = 0 there exists a Cr−2, or analytic diffeomorphism, which transforms F to the form ...
This textbook is aimed at newcomers to nonlinear dynamics and chaos, especially students taking a first course in the subject.
... Non-linear Oscillations, Dynamical Systems and Bifurcations of Vector Fields (Springer, Berlin, 1983) N.N. Bogolyubov, Yu.A. Mitropolsky, Asymptotic Methods in the Theory of Nonlinear Oscillations (Gordon and Breach/Hindustan Publ., New ...
In this book we have developed the asymptotic analysis of nonlinear dynamical systems.
This book uses a hands-on approach to nonlinear dynamics using commonly available software, including the free dynamical systems software Xppaut, Matlab (or its free cousin, Octave) and the Maple symbolic algebra system.
This book focuses on a central question in the field of complex systems: Given a fluctuating (in time or space), uni- or multi-variant sequentially measured set of experimental data (even noisy data), how should one analyse non ...
The selection of topics emphasizes bifurcation theory and topological analysis of dynamical systems. The book includes real-life problems and experiments as well as exercises and worked examples to test understanding.
This distinctive volume presents a clear, rigorous grounding in modern nonlinear integrable dynamics theory and applications in mathematical physics, and an introduction to timely leading-edge developments in the field — including some ...