Viability Theory

Author : Jean-Pierre Aubin
Publisher : Springer Science & Business Media
ISBN 13 : 0817649107
Total Pages : 558 pages
Book Rating : 4.04/5 ( download)

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Download or read book Viability Theory written by Jean-Pierre Aubin and published by Springer Science & Business Media. This book was released on 2009-05-28 with total page 558 pages. Available in PDF, EPUB and Kindle. Book excerpt: "The book is a compendium of the state of knowledge about viability...Mathematically, the book should be accessible to anyone who has had basic graduate courses in modern analysis and functional analysis...The concepts are defined and many proofs of the requisite results are reproduced here, making the present book essentially self-contained." —Bulletin of the AMS "Because of the wide scope, the book is an ideal reference for people encountering problems related to viability theory in their research...It gives a very thorough mathematical presentation. Very useful for anybody confronted with viability constraints." —Mededelingen van het Wiskundig Genootschap

Author : Jean Pierre Aubin
Publisher :
ISBN 13 :
Total Pages : 584 pages
Book Rating : 4.30/5 ( download)

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Download or read book Viability Theory written by Jean Pierre Aubin and published by . This book was released on 1991 with total page 584 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work examines viability theory and its applications to control theory and differential games. The emphasis is on the construction of feedbacks and dynamical systems by myopic optimization methods. Systems of first-order partial differential inclusions, whose solutions are feedbacks, are constructed and investigated. Basic results are then extended to the case of fuzzy control problems, distributed control problems, and control systems with delays and memory. Aimed at graduate students and research mathematicians, both pure and applied, this book offers specialists in control and nonlinear systems tools to take into account general state constraints. Viability theory also allows researchers in other disciplinesâartificial intelligence, economics, game theory, theoretical biology, population genetics, cognitive sciencesâto go beyond deterministic models by studying them in a dynamical or evolutionary perspective in an uncertain environment. "The book is a compendium of the state of knowledge about viability...Mathematically, the book should be accessible to anyone who has had basic graduate courses in modern analysis and functional analysisâ¦The concepts are defined and many proofs of the requisite results are reproduced here, making the present book essentially self-contained." (Bulletin of the AMS) "Because of the wide scope, the book is an ideal reference for people encountering problems related to viability theory in their researchâ¦It gives a very thorough mathematical presentation. Very useful for anybody confronted with viability constraints." (Mededelingen van het Wiskundig Genootschap)

Author : J.-P. Aubin
Publisher : Springer Science & Business Media
ISBN 13 : 3642695124
Total Pages : 353 pages
Book Rating : 4.24/5 ( download)

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Download or read book Differential Inclusions written by J.-P. Aubin and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 353 pages. Available in PDF, EPUB and Kindle. Book excerpt: A great impetus to study differential inclusions came from the development of Control Theory, i.e. of dynamical systems x'(t) = f(t, x(t), u(t)), x(O)=xo "controlled" by parameters u(t) (the "controls"). Indeed, if we introduce the set-valued map F(t, x)= {f(t, x, u)}ueu then solutions to the differential equations (*) are solutions to the "differen tial inclusion" (**) x'(t)EF(t, x(t)), x(O)=xo in which the controls do not appear explicitely. Systems Theory provides dynamical systems of the form d x'(t)=A(x(t)) dt (B(x(t))+ C(x(t)); x(O)=xo in which the velocity of the state of the system depends not only upon the x(t) of the system at time t, but also on variations of observations state B(x(t)) of the state. This is a particular case of an implicit differential equation f(t, x(t), x'(t)) = 0 which can be regarded as a differential inclusion (**), where the right-hand side F is defined by F(t, x)= {vlf(t, x, v)=O}. During the 60's and 70's, a special class of differential inclusions was thoroughly investigated: those of the form X'(t)E - A(x(t)), x (0) =xo where A is a "maximal monotone" map. This class of inclusions contains the class of "gradient inclusions" which generalize the usual gradient equations x'(t) = -VV(x(t)), x(O)=xo when V is a differentiable "potential". 2 Introduction There are many instances when potential functions are not differentiable

Author : Guillaume Deffuant
Publisher : Springer
ISBN 13 : 3642204236
Total Pages : 227 pages
Book Rating : 4.34/5 ( download)

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Download or read book Viability and Resilience of Complex Systems written by Guillaume Deffuant and published by Springer. This book was released on 2011-08-03 with total page 227 pages. Available in PDF, EPUB and Kindle. Book excerpt: One common characteristics of a complex system is its ability to withstand major disturbances and the capacity to rebuild itself. Understanding how such systems demonstrate resilience by absorbing or recovering from major external perturbations requires both quantitative foundations and a multidisciplinary view on the topic. This book demonstrates how new methods can be used to identify the actions favouring the recovery from perturbations. Examples discussed include bacterial biofilms resisting detachment, grassland savannahs recovering from fire, the dynamics of language competition and Internet social networking sites overcoming vandalism. The reader is taken through an introduction to the idea of resilience and viability and shown the mathematical basis of the techniques used to analyse systems. The idea of individual or agent-based modelling of complex systems is introduced and related to analytically tractable approximations of such models. A set of case studies illustrates the use of the techniques in real applications, and the final section describes how one can use new and elaborate software tools for carrying out the necessary calculations. The book is intended for a general scientific audience of readers from the natural and social sciences, yet requires some mathematics to gain a full understanding of the more theoretical chapters. It is an essential point of reference for those interested in the practical application of the concepts of resilience and viability

Author : Jean-Pierre Aubin
Publisher : Springer
ISBN 13 : 9783642645426
Total Pages : 510 pages
Book Rating : 4.29/5 ( download)

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Download or read book Dynamic Economic Theory written by Jean-Pierre Aubin and published by Springer. This book was released on 2013-11-13 with total page 510 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is intended to provide economists with mathematical tools necessary to handle the concepts of evolution under uncertainty and adaption arising in economics, pursuing the Arrow-Debreu-Hahn legacy. It applies the techniques of viability theory to the study of economic systems evolving under contingent uncertainty, faced with scarcity constraints, and obeying various implementation of the inertia principle. The book illustrates how new tools can be used to move from static analysis, built on concepts of optima, equilibria and attractors to a contingent dynamic framework.

Author : Ovidiu Carja
Publisher : Elsevier
ISBN 13 : 9780080521664
Total Pages : 356 pages
Book Rating : 4.65/5 ( download)

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Download or read book Viability, Invariance and Applications written by Ovidiu Carja and published by Elsevier. This book was released on 2007-07-18 with total page 356 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book is an almost self-contained presentation of the most important concepts and results in viability and invariance. The viability of a set K with respect to a given function (or multi-function) F, defined on it, describes the property that, for each initial data in K, the differential equation (or inclusion) driven by that function or multi-function) to have at least one solution. The invariance of a set K with respect to a function (or multi-function) F, defined on a larger set D, is that property which says that each solution of the differential equation (or inclusion) driven by F and issuing in K remains in K, at least for a short time. The book includes the most important necessary and sufficient conditions for viability starting with Nagumo’s Viability Theorem for ordinary differential equations with continuous right-hand sides and continuing with the corresponding extensions either to differential inclusions or to semilinear or even fully nonlinear evolution equations, systems and inclusions. In the latter (i.e. multi-valued) cases, the results (based on two completely new tangency concepts), all due to the authors, are original and extend significantly, in several directions, their well-known classical counterparts. New concepts for multi-functions as the classical tangent vectors for functions Provides the very general and necessary conditions for viability in the case of differential inclusions, semilinear and fully nonlinear evolution inclusions Clarifying examples, illustrations and numerous problems, completely and carefully solved Illustrates the applications from theory into practice Very clear and elegant style

Author : Guillaume Deffuant
Publisher : Springer Science & Business Media
ISBN 13 : 3642204228
Total Pages : 227 pages
Book Rating : 4.27/5 ( download)

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Download or read book Viability and Resilience of Complex Systems written by Guillaume Deffuant and published by Springer Science & Business Media. This book was released on 2011-08-03 with total page 227 pages. Available in PDF, EPUB and Kindle. Book excerpt: One common characteristics of a complex system is its ability to withstand major disturbances and the capacity to rebuild itself. Understanding how such systems demonstrate resilience by absorbing or recovering from major external perturbations requires both quantitative foundations and a multidisciplinary view on the topic. This book demonstrates how new methods can be used to identify the actions favouring the recovery from perturbations. Examples discussed include bacterial biofilms resisting detachment, grassland savannahs recovering from fire, the dynamics of language competition and Internet social networking sites overcoming vandalism. The reader is taken through an introduction to the idea of resilience and viability and shown the mathematical basis of the techniques used to analyse systems. The idea of individual or agent-based modelling of complex systems is introduced and related to analytically tractable approximations of such models. A set of case studies illustrates the use of the techniques in real applications, and the final section describes how one can use new and elaborate software tools for carrying out the necessary calculations. The book is intended for a general scientific audience of readers from the natural and social sciences, yet requires some mathematics to gain a full understanding of the more theoretical chapters. It is an essential point of reference for those interested in the practical application of the concepts of resilience and viability

Author : William F. Morris
Publisher : Sinauer Associates Incorporated
ISBN 13 : 9780878935468
Total Pages : 480 pages
Book Rating : 4.60/5 ( download)

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Download or read book Quantitative Conservation Biology written by William F. Morris and published by Sinauer Associates Incorporated. This book was released on 2002-01-01 with total page 480 pages. Available in PDF, EPUB and Kindle. Book excerpt: The goal of this book is to provide practical, intelligible, and intuitive explanations of population modelling to empirical ecologists and conservation biologists. Modelling methods that do not require large amounts of data (typically unavailable for endangered species) are emphasised. As such, the book is appropriate for undergraduate and graduate students interested in quantitative conservation biology, managers charged with preserving endangered species, and, in short, for any conservation biologist or ecologist seeking to better understand the analysis and modelling of population data.

Author : Jean-Pierre AUBIN
Publisher : Springer
ISBN 13 : 9783642166853
Total Pages : 830 pages
Book Rating : 4.57/5 ( download)

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Download or read book Viability Theory written by Jean-Pierre AUBIN and published by Springer. This book was released on 2013-01-02 with total page 830 pages. Available in PDF, EPUB and Kindle. Book excerpt: Viability theory designs and develops mathematical and algorithmic methods for investigating the adaptation to viability constraints of evolutions governed by complex systems under uncertainty that are found in many domains involving living beings, from biological evolution to economics, from environmental sciences to financial markets, from control theory and robotics to cognitive sciences. It involves interdisciplinary investigations spanning fields that have traditionally developed in isolation. The purpose of this book is to present an initiation to applications of viability theory, explaining and motivating the main concepts and illustrating them with numerous numerical examples taken from various fields.

Author : Thierry Burger-Helmchen
Publisher : Routledge
ISBN 13 : 1135103410
Total Pages : 377 pages
Book Rating : 4.15/5 ( download)

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Download or read book The Economics of Creativity written by Thierry Burger-Helmchen and published by Routledge. This book was released on 2013-02-11 with total page 377 pages. Available in PDF, EPUB and Kindle. Book excerpt: Understanding the economic implication of creative individuals and firms is at the heart of the new economy and of related fields such as the economics of knowledge, the economics of science and innovation management. This book brings together a panel of theoretical and empirical contributions which address the generation of creative ideas and their transformation into products and services by firms or universities, as well as the interplay of those organizations in networks and markets. The word ‘creativity’ has been used a great deal recently in relation to efforts to recover from the global financial crisis and re-launch economic activity. Little has been added to explain how and why an economic approach of creativity is useful and necessary. It is useful to understand how the most creative people work and think, and how to foster their creative productivity. It is useful to understand how organizations integrate and exploit creative ideas. It is useful to understand how market mechanisms can handle creativity and how policies must be adapted. It is necessary in the light of the recent economic crises that made innovation, invention and creativity the basis of a new industrialization and fuel for a new economic development. This new book assesses the economic impact of creativity, defining the term and then going on to explore theoretically and practically the economic consequences of creativity through a range of themes including: creativity and evolutionary theories of technological change; creativity and organizational learning; creativity and technological policy; and creativity and economics of networks. This volume offers a rich source of inspiration and ideas for the pursuit of research which merges economic tradition and management perspectives.