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osipenko g symbolic analysis dynamical systems 2025

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Textbook in PDF format This book was written on the basis of a special course on Computer Simulation of Dynamic Systems. The lectures were devoted to methods for studying the global properties of dynamic systems and differ from well-known monographs in the original research method called the Symbolic Image of Dynamic System. The symbolic image is a directed graph that approximates a dynamic system by discretizing phase space. The dynamics produced by such a graph reflects the dynamics of the system. The symbolic image provides a unified basis for applying various techniques to dynamic systems whether they are continuous or discrete in time. By converting the system’s flow into a graph, researchers can express their methods in terms of graph algorithms. Symbolic images are both an effective theoretical tool and the foundation for computer-oriented techniques for numerically studying non-local properties of systems. The monograph is a continuation of “Dynamical systems, graphs, and algorithms,” Lecture Notes in Mathematics, Volume 1889 (2006). If the results have already been proven in that book, they are presented here without proof. Proofs of the remaining results can be found in full. We present current theoretical and applied results on symbolic image analysis for dynamic systems. This material fully reflects the current state of research in this area. A symbolic image is an effective tool for theory and the basis for numerical methods for investigating non-local system properties. From a computing perspective, this approach based on graphs offers significant benefits: once a symbolic image has been established, all future research can be focused on analyzing the graph. Lectures include numerous illustrative examples for comprehension. The book is aimed at researchers studying dynamic systems and their application in various scientific and technical fields, including engineering, physics, chemistry, biology, economy, and demography. Lectures will be of interest to students, graduate students, and teachers of natural science departments

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osipenko g symbolic analysis dynamical systems 2025

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