Dynamical System Theory in Biology: Stability theory and its applications
Author : Robert Rosen
Publisher : John Wiley & Sons
Page : 330 pages
File Size : 14,38 MB
Release : 1970
Category : Science
ISBN :
Dynamical System Theory in Biology: Stability theory and its applications
Author : Robert Rosen
Publisher : John Wiley & Sons
Page : 328 pages
File Size : 49,23 MB
Release : 1970
Category : Science
ISBN :
Book Description
Dynamical Systems and Control
Author : Firdaus E. Udwadia
Publisher : CRC Press
Page : 450 pages
File Size : 23,58 MB
Release : 2004-05-10
Category : Mathematics
ISBN : 0203694589
Book Description
The 11th International Workshop on Dynamics and Control brought together scientists and engineers from diverse fields and gave them a venue to develop a greater understanding of this discipline and how it relates to many areas in science, engineering, economics, and biology. The event gave researchers an opportunity to investigate ideas and techniq
Stability Theory for Dynamic Equations on Time Scales
Author : Anatoly A. Martynyuk
Publisher : Birkhäuser
Page : 233 pages
File Size : 41,98 MB
Release : 2016-09-22
Category : Mathematics
ISBN : 3319422138
Book Description
This monograph is a first in the world to present three approaches for stability analysis of solutions of dynamic equations. The first approach is based on the application of dynamic integral inequalities and the fundamental matrix of solutions of linear approximation of dynamic equations. The second is based on the generalization of the direct Lyapunovs method for equations on time scales, using scalar, vector and matrix-valued auxiliary functions. The third approach is the application of auxiliary functions (scalar, vector, or matrix-valued ones) in combination with differential dynamic inequalities. This is an alternative comparison method, developed for time continuous and time discrete systems.In recent decades, automatic control theory in the study of air- and spacecraft dynamics and in other areas of modern applied mathematics has encountered problems in the analysis of the behavior of solutions of time continuous-discrete linear and/or nonlinear equations of perturbed motion. In the book “Men of Mathematics,” 1937, E.T.Bell wrote: “A major task of mathematics today is to harmonize the continuous and the discrete, to include them in one comprehensive mathematics, and to eliminate obscurity from both.”Mathematical analysis on time scales accomplishes exactly this. This research has potential applications in such areas as theoretical and applied mechanics, neurodynamics, mathematical biology and finance among others.
Differential Dynamical Systems, Revised Edition
Author : James D. Meiss
Publisher : SIAM
Page : 410 pages
File Size : 37,41 MB
Release : 2017-01-24
Category : Mathematics
ISBN : 161197464X
Book Description
Differential equations are the basis for models of any physical systems that exhibit smooth change. This book combines much of the material found in a traditional course on ordinary differential equations with an introduction to the more modern theory of dynamical systems. Applications of this theory to physics, biology, chemistry, and engineering are shown through examples in such areas as population modeling, fluid dynamics, electronics, and mechanics. Differential Dynamical Systems begins with coverage of linear systems, including matrix algebra; the focus then shifts to foundational material on nonlinear differential equations, making heavy use of the contraction-mapping theorem. Subsequent chapters deal specifically with dynamical systems concepts?flow, stability, invariant manifolds, the phase plane, bifurcation, chaos, and Hamiltonian dynamics. This new edition contains several important updates and revisions throughout the book. Throughout the book, the author includes exercises to help students develop an analytical and geometrical understanding of dynamics. Many of the exercises and examples are based on applications and some involve computation; an appendix offers simple codes written in Maple, Mathematica, and MATLAB software to give students practice with computation applied to dynamical systems problems.
Systems Theory with Engineering Applications
Author : Mihail Voicu
Publisher : Cambridge Scholars Publishing
Page : 250 pages
File Size : 38,58 MB
Release : 2021-09-09
Category : Language Arts & Disciplines
ISBN : 1527574555
Book Description
This book presents, in a rigorous and comprehensible way, the mathematical description and analysis of linear dynamic systems, and the controllability and observability of linear dynamic systems. It also details the stability of linear dynamic systems, automatic control systems, and nonlinear dynamic systems, and the optimal control of dynamic systems. The treatment is both systemic and synthetic, achieving rigorous and applicative solutions, and is illustrated with engineering examples. The book will appeal to scientists working in the practice of systems theory, engineering, automatic control, computer science, electrical engineering, electronics, and applied mathematics in biology and economics, as well as scientists working in education, research, design and industry.
Perspectives in Mathematical System Theory, Control, and Signal Processing
Author : Jan C. Willems
Publisher : Springer Science & Business Media
Page : 391 pages
File Size : 29,28 MB
Release : 2010-02-28
Category : Science
ISBN : 3540939172
Book Description
This Festschrift, published on the occasion of the sixtieth birthday of Yutaka - mamoto (‘YY’ as he is occasionally casually referred to), contains a collection of articles by friends, colleagues, and former Ph.D. students of YY. They are a tribute to his friendship and his scienti?c vision and oeuvre, which has been a source of inspiration to the authors. Yutaka Yamamoto was born in Kyoto, Japan, on March 29, 1950. He studied applied mathematics and general engineering science at the Department of Applied Mathematics and Physics of Kyoto University, obtaining the B.S. and M.Sc. degrees in 1972 and 1974. His M.Sc. work was done under the supervision of Professor Yoshikazu Sawaragi. In 1974, he went to the Center for Mathematical System T- ory of the University of Florida in Gainesville. He obtained the M.Sc. and Ph.D. degrees, both in Mathematics, in 1976 and 1978, under the direction of Professor Rudolf Kalman.
The Dynamic Systems of Basic Economic Growth Models
Author : Bjarne S. Jensen
Publisher : Springer Science & Business Media
Page : 358 pages
File Size : 45,99 MB
Release : 2012-02-02
Category : Mathematics
ISBN : 9401110360
Book Description
Two central problems in the pure theory of economic growth are analysed in this monograph: 1) the dynamic laws governing the economic growth processes, 2) the kinematic and geometric properties of the set of solutions to the dynamic systems. With allegiance to rigor and the emphasis on the theoretical fundamentals of prototype mathematical growth models, the treatise is written in the theorem-proof style. To keep the exposition orderly and as smooth as possible, the economic analysis has been separated from the purely mathematical issues, and hence the monograph is organized in two books. Regarding the scope and content of the two books, an "Introduction and Over view" has been prepared to offer both motivation and a brief account. The introduc tion is especially designed to give a recapitulation of the mathematical theory and results presented in Book II, which are used as the unifying mathematical framework in the analysis and exposition of the different economic growth models in Book I. Economists would probably prefer to go directly to Book I and proceed by consult ing the mathematical theorems of Book II in confirming the economic theorems in Book I. Thereby, both the independence and interdependence of the economic and mathematical argumentations are respected.
Nonlinear Dynamical Systems and Control
Author : Wassim M. Haddad
Publisher : Princeton University Press
Page : 975 pages
File Size : 12,84 MB
Release : 2011-09-19
Category : Mathematics
ISBN : 1400841046
Book Description
Nonlinear Dynamical Systems and Control presents and develops an extensive treatment of stability analysis and control design of nonlinear dynamical systems, with an emphasis on Lyapunov-based methods. Dynamical system theory lies at the heart of mathematical sciences and engineering. The application of dynamical systems has crossed interdisciplinary boundaries from chemistry to biochemistry to chemical kinetics, from medicine to biology to population genetics, from economics to sociology to psychology, and from physics to mechanics to engineering. The increasingly complex nature of engineering systems requiring feedback control to obtain a desired system behavior also gives rise to dynamical systems. Wassim Haddad and VijaySekhar Chellaboina provide an exhaustive treatment of nonlinear systems theory and control using the highest standards of exposition and rigor. This graduate-level textbook goes well beyond standard treatments by developing Lyapunov stability theory, partial stability, boundedness, input-to-state stability, input-output stability, finite-time stability, semistability, stability of sets and periodic orbits, and stability theorems via vector Lyapunov functions. A complete and thorough treatment of dissipativity theory, absolute stability theory, stability of feedback systems, optimal control, disturbance rejection control, and robust control for nonlinear dynamical systems is also given. This book is an indispensable resource for applied mathematicians, dynamical systems theorists, control theorists, and engineers.
Bifurcation Theory And Applications
Author : Shouhong Wang
Publisher : World Scientific
Page : 391 pages
File Size : 13,8 MB
Release : 2005-06-27
Category : Science
ISBN : 9814480592
Book Description
This book covers comprehensive bifurcation theory and its applications to dynamical systems and partial differential equations (PDEs) from science and engineering, including in particular PDEs from physics, chemistry, biology, and hydrodynamics.The book first introduces bifurcation theories recently developed by the authors, on steady state bifurcation for a class of nonlinear problems with even order nondegenerate nonlinearities, regardless of the multiplicity of the eigenvalues, and on attractor bifurcations for nonlinear evolution equations, a new notion of bifurcation.With this new notion of bifurcation, many longstanding bifurcation problems in science and engineering are becoming accessible, and are treated in the second part of the book. In particular, applications are covered for a variety of PDEs from science and engineering, including the Kuramoto-Sivashinsky equation, the Cahn-Hillard equation, the Ginzburg-Landau equation, reaction-diffusion equations in biology and chemistry, the Benard convection problem, and the Taylor problem. The applications provide, on the one hand, general recipes for other applications of the theory addressed in this book, and on the other, full classifications of the bifurcated attractor and the global attractor as the control parameters cross certain critical values, dictated usually by the eigenvalues of the linearized problems. It is expected that the book will greatly advance the study of nonlinear dynamics for many problems in science and engineering.
