Working With Dynamical Systems
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Stability of Dynamical Systems
In the analysis and synthesis of contemporary systems, engineers and scientists are frequently confronted with increasingly complex models that may simultaneously include components whose states evolve along continuous time and discrete instants; components whose descriptions may exhibit nonlinearities, time lags, transportation delays, hysteresis effects, and uncertainties in parameters; and components that cannot be described by various classical equations, as in the case of discrete-event systems, logic commands, and Petri nets. The qualitative analysis of such systems requires results for finite-dimensional and infinite-dimensional systems; continuous-time and discrete-time systems; continuous continuous-time and discontinuous continuous-time systems; and hybrid systems involving a mixture of continuous and discrete dynamics. Filling a gap in the literature, this textbook presents the first comprehensive stability analysis of all the major types of system models described above. Throughout the book, the applicability of the developed theory is demonstrated by means of many specific examples and applications to important classes of systems, including digital control systems, nonlinear regulator systems, pulse-width-modulated feedback control systems, artificial neural networks (with and without time delays), digital signal processing, a class of discrete-event systems (with applications to manufacturing and computer load balancing problems) and a multicore nuclear reactor model. The book covers the following four general topics: * Representation and modeling of dynamical systems of the types described above * Presentation of Lyapunov and Lagrange stability theory for dynamical systems defined on general metric spaces * Specialization of this stability theory to finite-dimensional dynamical systems * Specialization of this stability theory to infinite-dimensional dynamical systems Replete with exercises and requiring basic knowledge of linear algebra, analysis, and differential equations, the work may be used as a textbook for graduate courses in stability theory of dynamical systems. The book may also serve as a self-study reference for graduate students, researchers, and practitioners in applied mathematics, engineering, computer science, physics, chemistry, biology, and economics.
Working with Dynamical Systems
This book provides working tools for the study and design of nonlinear dynamical systems applicable in physics and engineering. It offers a broad-based introduction to this challenging area of study, taking an applications-oriented approach that emphasizes qualitative analysis and approximations rather than formal mathematics or simulation. The author, an internationally recognized authority in the field, makes extensive use of examples and includes executable Mathematica notebooks that may be used to generate new examples as hands-on exercises. The coverage includes discussion of mechanical models, chemical and ecological interactions, nonlinear oscillations and chaos, forcing and synchronization, spatial patterns and waves. Key Features: Written for a broad audience, avoiding dependence on mathematical formulations in favor of qualitative, constructive treatment Extensive use of physical and engineering applications Incorporates Mathematica notebooks for simulations and hands-on self-study Provides a gentle but rigorous introduction to real-world nonlinear problems Features a final chapter dedicated to applications of dynamical systems to spatial patterns The book is aimed at student and researchers in applied mathematics and mathematical modelling of physical and engineering problems. It teaches to see common features in systems of different origins, and to apply common methods of study without losing sight of complications and uncertainties related to their physical origin.
Dynamical Systems, Bifurcation Analysis and Applications
This book is the result of Southeast Asian Mathematical Society (SEAMS) School 2018 on Dynamical Systems and Bifurcation Analysis (DySBA). It addresses the latest developments in the field of dynamical systems, and highlights the importance of numerical continuation studies in tracking both stable and unstable steady states and bifurcation points to gain better understanding of the dynamics of the systems. The SEAMS School 2018 on DySBA was held in Penang from 6th to 13th August at the School of Mathematical Sciences, Universiti Sains Malaysia.The SEAMS Schools are part of series of intensive study programs that aim to provide opportunities for an advanced learning experience in mathematics via planned lectures, contributed talks, and hands-on workshop. This book will appeal to those postgraduates, lecturers and researchers working in the field of dynamical systems and their applications. Senior undergraduates in Mathematics will also find it useful.