Viability Theory
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| Author | : Jean Pierre Aubin |
| Publisher | : |
| Total Pages | : 584 |
| Release | : 1991 |
| Genre | : Differential inclusions |
| ISBN | : |
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 | : Jean-Pierre Aubin |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 558 |
| Release | : 2009-05-28 |
| Genre | : Science |
| ISBN | : 0817649107 |
"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 | : J.-P. Aubin |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 353 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 3642695124 |
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 Science & Business Media |
| Total Pages | : 227 |
| Release | : 2011-08-03 |
| Genre | : Social Science |
| ISBN | : 3642204228 |
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 |
| Total Pages | : 510 |
| Release | : 2013-11-13 |
| Genre | : Business & Economics |
| ISBN | : 9783642645426 |
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 | : Girol Karacaoglu |
| Publisher | : Springer |
| Total Pages | : 257 |
| Release | : 2019-01-28 |
| Genre | : Political Science |
| ISBN | : 9811361045 |
The distinctive contribution of this book is the formulation of an integrated social, environmental, and economic framework for public policy. This contribution is realised through investigations and conclusions in the following four domains: a formal stylised model that provides a platform for an integrated approach to public policy; a policy-informing simulation model that can be used to operationalise the public policy insights proposed in the stylised model; the implications of introducing fundamental (or radical) uncertainty and complexity into the policy framework; and the use of viability theory to demonstrate how one can think of and implement public policy in an uncertain and complex world, when the focus of policy needs to shift to building resilience to systemic risks. The book’s stylised model is constructed by weaving together threads from the wellbeing, human needs, complex systems, sustainable development, endogenous economic growth, directed technical change, and credit-based-money literatures. Throughout, the perspective is that of a policy adviser to a "wellbeing state", as distinct from a "welfare state". The key linkages or relationships in the model are supported by empirical evidence that draws on the wider literature in related fields.
| Author | : William F. Morris |
| Publisher | : Sinauer Associates Incorporated |
| Total Pages | : 480 |
| Release | : 2002-01-01 |
| Genre | : Science |
| ISBN | : 9780878935468 |
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 | : Steven R. Beissinger |
| Publisher | : University of Chicago Press |
| Total Pages | : 594 |
| Release | : 2002-05-04 |
| Genre | : Nature |
| ISBN | : 0226041786 |
Many of the world's leading conservation and population biologists evaluate what has become a key tool in estimating extinction risk and evaluating potential recovery strategies - population viability analysis, or PVA.
| Author | : Michael Thompson |
| Publisher | : Routledge |
| Total Pages | : 267 |
| Release | : 2018-06-27 |
| Genre | : Social Science |
| ISBN | : 0429980817 |
Why do people want what they want? Why does one person see the world as a place to control, while another feels controlled by the world? A useful theory of culture, the authors contend, should start with these questions, and the answers, given different historical conditions, should apply equally well to people of all times, places, and walks of life.Taking their cue from the pioneering work of anthropologist Mary Douglas, the authors of Cultural Theory have created a typology of five ways of life?egalitarianism, fatalism, individualism, hierarchy, and autonomy?to serve as an analytic tool in examining people, culture, and politics. They then show how cultural theorists can develop large numbers of falsifiable propositions.Drawing on parables, poetry, case studies, fiction, and the Great Books, the authors illustrate how cultural biases and social relationships interact in particular ways to yield life patterns that are viable, sustainable, and ultimately, changeable under certain conditions. Figures throughout the book show the dynamic quality of these ways of life and specifically illustrate the role of surprise in effecting small- and large-scale change.The authors compare Cultural Theory with the thought of master social theorists from Montesquieu to Stinchcombe and then reanalyze the classic works in the political culture tradition from Almond and Verba to Pye. Demonstrating that there is more to social life than hierarchy and individualism, the authors offer evidence from earlier studies showing that the addition of egalitarianism and fatalism facilitates cross-national comparisons.
| Author | : Utsa Patnaik |
| Publisher | : Columbia University Press |
| Total Pages | : 254 |
| Release | : 2016-11-01 |
| Genre | : Political Science |
| ISBN | : 0231542267 |
In A Theory of Imperialism, economists Utsa Patnaik and Prabhat Patnaik present a new theory of the origins and mechanics of capitalism that sounds an alarm about its ongoing viability. Their theory centers on trade between the core economies of the global North and the tropical and subtropical countries of the global South and considers how the Northern demand for commodities (such as agricultural products and oil) from the South has perpetuated and solidified an imperialist relationship. The Patnaiks explore the dynamics of this process and discuss innovations that could allow the economies of the South to achieve greater prosperity without damaging the economies of the North. The result is an original theory of imperialism that brings to light the crippling limitations of neoliberal capitalism. A Theory of Imperialism also includes a response by David Harvey, who interprets the agrarian system differently and sees other factors affecting trade between the North and the South. Their debate is one of the most provocative exchanges yet over the future of the global economy as resources grow thin, populations explode, and universal prosperity becomes ever more elusive.
