:a unified modelling approach to physics, control, biomechanics, neurodynamics and psycho-socio-economical dynamics
/ by Vladimir G. Ivancevic and Tijana T. Ivancevic
Dordrecht
: Springer,
, c2006.
xxiii, 822 p. , ill. , 25 cm.
(International series on microprocessor-based and intelligent systems engineering v. 31)
Electronic
Includes bibliographical references and index.
"This volume presents a comprehensive introduction into rigorous geometrical dynamics of complex systems of various natures. By "complex systems", in this book are meant high-dimensional nonlinear systems, which can be (but not necessarily are) adaptive. This monograph proposes a unified geometrical approach to dynamics of complex systems of various kinds: engineering, physical, biophysical, psychophysical, sociophysical, econophysical, etc. As their names suggest, all these multi-input multi-output (MIMO) systems have something in common: the underlying physics. Using sophisticated machinery composed of differential geometry, topology and path integrals, this book proposes a unified approach to complex dynamics - of predictive power much greater than the currently popular "soft-science" approach to complex systems. The main objective of this book is to show that high-dimensional nonlinear systems in "real life" can be modeled and analyzed using rigorous mathematics, which enables their complete predictability and controllability, as if they were linear systems."--BOOK JACKET.
1. Modern geometrical machinery -- 2. Dynamics of complex systems -- 3. Appendix : tensors and functions.