Vladimir G. Ivancevic, Tijana T. Ivancevic

Geometrical Dynamics of Complex Systems

A Unified Modelling Approach to Physics, Control, Biomechanics, Neurodynamics and Psycho-Socio-Economical Dynamics

• Gebundenes Buch

Produktbeschreibung

Geometrical Dynamics of Complex Systems is a graduate level monographic textbook. Itrepresentsacomprehensiveintroductionintorigorousgeometrical dynamicsofcomplexsystemsofvariousnatures. By complexsystems ,inthis book are meant high dimensional nonlinear systems, which can be (but not necessarily are) adaptive. This monograph proposes a uni?ed geometrical - proachtodynamicsofcomplexsystemsofvariouskinds: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. However, instead of dealing with the pop- 1 ular soft complexity philosophy , we rather propose a rigorous geometrical and topological approach. We believe that our rigorous approach has much greater predictive power than the soft one. We argue that science and te- nology is all about prediction and control. Observation, understanding and explanation are important in education at undergraduate level, but after that it should be all prediction and control. The main objective of this book is to show that high dimensional nonlinear systems and processes of real life can be modelled and analyzed using rigorous mathematics, which enables their complete predictability and controllability, as if they were linear systems. It is well known that linear systems, which are completely predictable and controllable by de?nition live only in Euclidean spaces (of various - mensions). They are as simple as possible, mathematically elegant and fully elaborated from either scienti?c or engineering side. However, in nature, no- ing is linear. In reality, everything has a certain degree of nonlinearity, which means: unpredictability, with subsequent uncontrollability.

Produktdetails

• Intelligent Systems, Control and Automation: Science and Engineering 31
• Verlag: Springer / Springer Netherlands
• Artikelnr. des Verlages: 978-1-4020-4544-8
• 2006
• Seitenzahl: 852
• Erscheinungstermin: 18. Januar 2006
• Englisch
• Abmessung: 241mm x 160mm x 50mm
• Gewicht: 1425g
• ISBN-13: 9781402045448
• ISBN-10: 1402045441
• Artikelnr.: 24535177

Autorenporträt

Vladimir G. Ivancevic, Defence Science and Technology Organisation, Adelaide, SA, Australia / Tijana T. Ivancevic, The University of Adelaide, SA, Australia

Inhaltsangabe

From the contents

Modern Geometrical Machinery.- Introduction.- Smooth Manifolds.- Fibre Bundles.- Jet Spaces.- Path Integrals: Extending Smooth Geometrical Machinery.- Dynamics of High -Dimensional Nonlinear Systems.- Mechanical Systems. Physical Field Systems.- Nonlinear Control Systems.- Human - Like Biomechanics.- Neurodynamics.- Psycho -Socio - Economic Dynamics.- Appendix: Tensors and Functors.- Elements of Classical Tensor Analysis.- Categories and Functors.- References.- Index.

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Rezensionen

From the reviews:

"As it is mentioned in the preface this is 'a graduate-level monographical textbook. It represents a comprehensive introduction into rigorous geometrical dynamics of complex systems of various natures'. ... This book has to be recommended for graduates in applied mathematics who are interested in basics of modern mathematical methods mostly based on geometry." (Iskander A. Taimanov, Zentralblatt MATH, Vol. 1092 (18), 2006)