Deepen Your Students' Understanding of Oscillations through Interactive ExperimentsSimulations of Oscillatory Systems: with Award-Winning Software, Physics of Oscillations provides a hands-on way of visualizing and understanding the fundamental concepts of the physics of oscillations. Both the textbook and software are designed as exploration-orien
This book briefly discusses the main provisions of the theory of modeling. It also describes in detail the methodology for constructing computer models of dynamic systems using the Wolfram visual modeling environment, SystemModeler, and provides illustrative examples of solving problems of mechanics and hydraulics. Intended for students and professionals in the field, the book also serves as a supplement to university courses in modeling and simulation of dynamic systems.
Rhythms of the heart and of the nervous and endocrine system, breathing, locomotory movements, sleep, circadian rhythms and tissue cell cycles are major elements of the temporal order of man. The dynamics of these systems are characterized by changes in the properties of an oscillator, transitions from oscillatory states into chaotic or stationary states, and vice versa, coupling or uncoupling between two or more oscillators. Any deviation from the normal range to either more or less ordered states may be defined as temporal disorder. Pathological changes of temporal organization, such as tremor, epileptic seizures, Cheyne-Stokes breathing, cardiac arrhythmicities and circadian desynchronization, may be caused by small changes in the order (control) parameters. One major aspect of the symposium was the analysis of characteristic features of these temporal control systems, including nonlinear dynamics of interactions, positive, negative and mixed feedback systems, temporal delays, and their mathematical description and modelling. The ultimate goal is a better understanding of the principles of temporal organization in order to treat periodic diseases or other perturbations of "normal" dynamics in human oscillatory systems.
Numerical simulation and modelling have been growing in importance and seeing steadily increasing practical application. The proliferation of applications and physical domains for which simulation technologies are now needed, compounded by generally increased complexity, has expanded the scope of numerical simulation and modelling within CAD and spurred new research directions. Numerical Simulation and Modelling of Electronic and Biochemical Systems provides an introduction to the fundamentals of numerical simulation, and to the basics of modelling electronic circuits and biochemical reactions. The emphasis is on capturing a minimal set of important concepts succinctly, but concretely enough that the reader will be left with an adequate foundation for further independent exploration. Starting from mathematical models of basic electronic elements, circuits are modelled as nonlinear differential-algebraic equation (DAE) systems. Two basic techniques - quiescent steady state and transient - for solving these differential equations systems are then developed. It is then shown how biochemical reactions can also be modelled deterministically as DAEs. Following this, frequency domain techniques for finding sinusoidal steady states of linear DAEs are developed, as are direct and adjoint techniques for computing parameter sensitivities and the effects of stationary random noise. For readers interested in a glimpse of topics beyond these basics, an introduction to nonlinear periodic steady state methods (harmonic balance and shooting) and the multitime partial differential equation formulation is provided. Also provided is an overview of model order reduction, an important topic of current research that has roots in numerical simulation algorithms. Finally, sample applications of nonlinear oscillator macromodels - in circuits (PLLs), biochemical reaction-diffusion systems and nanoelectronics - are presented.
Written for those interested in designing machines to perform intelligent functions & those interested in studying how these functions are performed by living organisms,this bk dicusses the mathematical structure & functional significance of neural oscil
A rich variety of books devoted to dynamical chaos, solitons, self-organization has appeared in recent years. These problems were all considered independently of one another. Therefore many of readers of these books do not suspect that the problems discussed are divisions of a great generalizing science - the theory of oscillations and waves. This science is not some branch of physics or mechanics, it is a science in its own right. It is in some sense a meta-science. In this respect the theory of oscillations and waves is closest to mathematics. In this book we call the reader's attention to the present-day theory of non-linear oscillations and waves. Oscillatory and wave processes in the systems of diversified physical natures, both periodic and chaotic, are considered from a unified poin t of view . The relation between the theory of oscillations and waves, non-linear dynamics and synergetics is discussed. One of the purposes of this book is to convince reader of the necessity of a thorough study popular branches of of the theory of oscillat ions and waves, and to show that such science as non-linear dynamics, synergetics, soliton theory, and so on, are, in fact , constituent parts of this theory. The primary audiences for this book are researchers having to do with oscillatory and wave processes, and both students and post-graduate students interested in a deep study of the general laws and applications of the theory of oscillations and waves.
