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This book, along with its companion volume, Nonlinear Dynamics New Directions: Models and Applications, covers part of the vast spectrum of interests of Professor Valentin Afraimovich, which range from fractal analysis to very specific applications of the theory of dynamical systems to biology. This first volume is devoted to fundamental aspects and includes a number of important new contributions as well as some review articles that emphasize new development prospects. The second volume contains mostly new applications of the theory of dynamical systems to both engineering and biology. Contributors to the two volumes, all of them academically related to Professor Afraimovich, are among the most prominent specialists in nonlinear dynamics. The topics addressed in the two volumes include a rigorous treatment of fluctuations in dynamical systems, topics in fractal analysis, studies of the transient dynamics in biological networks, synchronization in lasers, and control of chaotic systems, among others.
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