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Control and Chaos / Kevin Judd ; SpringerLink (Online service) ; Alistair I. Mees ; Kok Lay Teo ; Thomas L. Vincent / Bâle (CHE) ; Boston, MA : Birkhäuser (1997)
Titre : Control and Chaos Type de document : document électronique Auteurs : Kevin Judd ; SpringerLink (Online service) ; Alistair I. Mees ; Kok Lay Teo ; Thomas L. Vincent Editeur : Bâle (CHE) ; Boston, MA : Birkhäuser Année de publication : 1997 Collection : Mathematical Modelling num. 8 Importance : 342 p Présentation : online resource ISBN/ISSN/EAN : 978-1-4612-2446-4 Langues : Anglais (eng) Tags : Mathematics Dynamics Ergodic theory System theory Systems Theory Control Dynamical Systems and Ergodic Theory Résumé : This volume contains the proceedings of the US-Australia workshop on Control and Chaos held in Honolulu, Hawaii from 29 June to 1 July, 1995. The workshop was jointly sponsored by the National Science Foundation (USA) and the Department of Industry, Science and Technology (Australia) under the US-Australia agreement. Control and Chaos-it brings back memories of the endless reruns of "Get Smart" where the good guys worked for Control and the bad guys were associated with Chaos. In keeping with current events, Control and Chaos are no longer adversaries but are now working together. In fact, bringing together workers in the two areas was the focus of the workshop. The objective of the workshop was to bring together experts in dynamical systems theory and control theory, and applications workers in both fields, to focus on the problem of controlling nonlinear and potentially chaotic systems using limited control effort. This involves finding and using orbits in nonlinear systems which can take a system from one region of state space to other regions where we wish to stabilize the system. Control is used to generate useful chaotic trajectories where they do not exist, and to identify and take advantage of useful ones where they do exist. A controller must be able to nudge a system into a proper chaotic orbit and know when to come off that orbit. Also, it must be able to identify regions of state space where feedback control will be effective Note de contenu : Understanding Complex Dynamics -- Triangulating Noisy Dynamical Systems -- Attractor Reconstruction and Control Using Interspike Intervals -- Modeling Chaos from Experimental Data -- Chaos in Symplectic Discretizations of the Pendulum and Sine-Gordon Equations -- Collapsing Effects in Computation of Dynamical Systems -- Bifurcations in the Falkner-Skan equation -- Some Characterisations of Low-dimensional Dynamical Systems with Time-reversal Symmetry -- Controlling Complex Systems -- Control of Chaos by Means of Embedded Unstable Periodic Orbits -- Notch Filter Feedback Control for k-Period Motion in a Chaotic System -- Targeting and Control of Chaos -- Adaptive Nonlinear Control: A Lyapunov Approach -- Creating and Targeting Periodic Orbits -- Dynamical Systems, Optimization, and Chaos -- Combined Controls for Noisy Chaotic Systems -- Complex Dynamics in Adaptive Systems -- Hitting Times to a Target for the Baker?s Map -- Applications -- Controllable Targets Near a Chaotic Attractor -- The Dynamics of Evolutionary Stable Strategies -- Nitrogen Cycling and the Control of Chaos in a Boreal Forest Model -- Self-organization Dynamics in Chaotic Neural Networks Permalink : https://genes.bibli.fr/index.php?lvl=notice_display&id=127090 Control and Chaos [document électronique] / Kevin Judd ; SpringerLink (Online service) ; Alistair I. Mees ; Kok Lay Teo ; Thomas L. Vincent . - Bâle (CHE) ; Boston, MA : Birkhäuser, 1997 . - 342 p : online resource. - (Mathematical Modelling; 8) .
ISBN : 978-1-4612-2446-4
Langues : Anglais (eng)
Tags : Mathematics Dynamics Ergodic theory System theory Systems Theory Control Dynamical Systems and Ergodic Theory Résumé : This volume contains the proceedings of the US-Australia workshop on Control and Chaos held in Honolulu, Hawaii from 29 June to 1 July, 1995. The workshop was jointly sponsored by the National Science Foundation (USA) and the Department of Industry, Science and Technology (Australia) under the US-Australia agreement. Control and Chaos-it brings back memories of the endless reruns of "Get Smart" where the good guys worked for Control and the bad guys were associated with Chaos. In keeping with current events, Control and Chaos are no longer adversaries but are now working together. In fact, bringing together workers in the two areas was the focus of the workshop. The objective of the workshop was to bring together experts in dynamical systems theory and control theory, and applications workers in both fields, to focus on the problem of controlling nonlinear and potentially chaotic systems using limited control effort. This involves finding and using orbits in nonlinear systems which can take a system from one region of state space to other regions where we wish to stabilize the system. Control is used to generate useful chaotic trajectories where they do not exist, and to identify and take advantage of useful ones where they do exist. A controller must be able to nudge a system into a proper chaotic orbit and know when to come off that orbit. Also, it must be able to identify regions of state space where feedback control will be effective Note de contenu : Understanding Complex Dynamics -- Triangulating Noisy Dynamical Systems -- Attractor Reconstruction and Control Using Interspike Intervals -- Modeling Chaos from Experimental Data -- Chaos in Symplectic Discretizations of the Pendulum and Sine-Gordon Equations -- Collapsing Effects in Computation of Dynamical Systems -- Bifurcations in the Falkner-Skan equation -- Some Characterisations of Low-dimensional Dynamical Systems with Time-reversal Symmetry -- Controlling Complex Systems -- Control of Chaos by Means of Embedded Unstable Periodic Orbits -- Notch Filter Feedback Control for k-Period Motion in a Chaotic System -- Targeting and Control of Chaos -- Adaptive Nonlinear Control: A Lyapunov Approach -- Creating and Targeting Periodic Orbits -- Dynamical Systems, Optimization, and Chaos -- Combined Controls for Noisy Chaotic Systems -- Complex Dynamics in Adaptive Systems -- Hitting Times to a Target for the Baker?s Map -- Applications -- Controllable Targets Near a Chaotic Attractor -- The Dynamics of Evolutionary Stable Strategies -- Nitrogen Cycling and the Control of Chaos in a Boreal Forest Model -- Self-organization Dynamics in Chaotic Neural Networks Permalink : https://genes.bibli.fr/index.php?lvl=notice_display&id=127090 Dynamics of Complex Interconnected Biological Systems / Thomas L. Vincent ; SpringerLink (Online service) ; Alistair I. Mees ; Leslie S. Jennings / Bâle (CHE) ; Boston, MA : Birkhäuser (1990)
Titre : Dynamics of Complex Interconnected Biological Systems Type de document : document électronique Auteurs : Thomas L. Vincent ; SpringerLink (Online service) ; Alistair I. Mees ; Leslie S. Jennings Editeur : Bâle (CHE) ; Boston, MA : Birkhäuser Année de publication : 1990 Collection : Mathematical Modelling num. 6 Importance : XII, 334 p Présentation : online resource ISBN/ISSN/EAN : 978-1-4684-6784-0 Langues : Anglais (eng) Tags : Mathematics Applied mathematics Engineering mathematics Mathematical models Biomathematics Mathematical and Computational Biology Mathematical Modeling and Industrial Mathematics Applications of Mathematics Résumé : This volume contains the proceedings of the U.S. Australia workshop on Complex Interconnected Biological Systems held in Albany, Western Australia January 1-5, 1989. The workshop was jointly sponsored by the Department of Industry, Trade and Commerce (Australia), and the Na tional Science Foundation (USA) under the US-Australia agreement. Biological systems are typically hard to study mathematically. This is particularly so in the case of systems with strong interconnections, such as ecosystems or networks of neurons. In the past few years there have been substantial improvements in the mathematical tools available for study ing complexity. Theoretical advances include substantially improved un derstanding of the features of nonlinear systems that lead to important behaviour patterns such as chaos. Practical advances include improved modelling techniques, and deeper understanding of complexity indicators such as fractal dimension. Game theory is now playing an increasingly important role in under standing and describing evolutionary processes in interconnected systems. The strategies of individuals which affect each other's fitness may be incor porated into models as parameters. Strategies which have the property of evolutionary stabilty result from particular parameter values which may be the main feature of living determined using game theoretic methods. Since systems is that they evolve, it seems appropriate that any model used to describe such systems should have this feature as well. Evolutionary game theory should lead the way in the development of such methods Note de contenu : I Modelling -- Modelling Biological Systems -- A Length-Structured Model of the Western Rock Lobster Fishery of Western Australia -- Legumes at Loggerheads: Modelling Competition Between two Strains of Sub-Clover -- Two Dimensional Pattern Formation in a Chemotactic System -- Mathematical Modelling of the Control of Blood Glucose Levels in Diabetics by Insulin Infusion -- II Tools -- Modelling Complex Systems -- Detecting Folds in Chaotic Processes by Mapping the Convex Hull -- Chaos in Complex Systems -- A Chaotic System: Discretization and Control -- Impulsive Evolution Equations and Population Models -- Scaling as a Tool for the Analysis of Biological Models -- A Numerical Algorithm for Constrained Optimal Control Problems with Applications to Harvesting -- III Games -- Strategy Dynamics and the Ess -- Community Organization under Predator-Prey Co-Evolution -- The Exploiters Conservationists Game: how to be an Effective Conservationist -- Analysing the Harvesting Game or why are there so Many Kinds of Fishing Vessels in the Fleet? Permalink : https://genes.bibli.fr/index.php?lvl=notice_display&id=127604 Dynamics of Complex Interconnected Biological Systems [document électronique] / Thomas L. Vincent ; SpringerLink (Online service) ; Alistair I. Mees ; Leslie S. Jennings . - Bâle (CHE) ; Boston, MA : Birkhäuser, 1990 . - XII, 334 p : online resource. - (Mathematical Modelling; 6) .
ISBN : 978-1-4684-6784-0
Langues : Anglais (eng)
Tags : Mathematics Applied mathematics Engineering mathematics Mathematical models Biomathematics Mathematical and Computational Biology Mathematical Modeling and Industrial Mathematics Applications of Mathematics Résumé : This volume contains the proceedings of the U.S. Australia workshop on Complex Interconnected Biological Systems held in Albany, Western Australia January 1-5, 1989. The workshop was jointly sponsored by the Department of Industry, Trade and Commerce (Australia), and the Na tional Science Foundation (USA) under the US-Australia agreement. Biological systems are typically hard to study mathematically. This is particularly so in the case of systems with strong interconnections, such as ecosystems or networks of neurons. In the past few years there have been substantial improvements in the mathematical tools available for study ing complexity. Theoretical advances include substantially improved un derstanding of the features of nonlinear systems that lead to important behaviour patterns such as chaos. Practical advances include improved modelling techniques, and deeper understanding of complexity indicators such as fractal dimension. Game theory is now playing an increasingly important role in under standing and describing evolutionary processes in interconnected systems. The strategies of individuals which affect each other's fitness may be incor porated into models as parameters. Strategies which have the property of evolutionary stabilty result from particular parameter values which may be the main feature of living determined using game theoretic methods. Since systems is that they evolve, it seems appropriate that any model used to describe such systems should have this feature as well. Evolutionary game theory should lead the way in the development of such methods Note de contenu : I Modelling -- Modelling Biological Systems -- A Length-Structured Model of the Western Rock Lobster Fishery of Western Australia -- Legumes at Loggerheads: Modelling Competition Between two Strains of Sub-Clover -- Two Dimensional Pattern Formation in a Chemotactic System -- Mathematical Modelling of the Control of Blood Glucose Levels in Diabetics by Insulin Infusion -- II Tools -- Modelling Complex Systems -- Detecting Folds in Chaotic Processes by Mapping the Convex Hull -- Chaos in Complex Systems -- A Chaotic System: Discretization and Control -- Impulsive Evolution Equations and Population Models -- Scaling as a Tool for the Analysis of Biological Models -- A Numerical Algorithm for Constrained Optimal Control Problems with Applications to Harvesting -- III Games -- Strategy Dynamics and the Ess -- Community Organization under Predator-Prey Co-Evolution -- The Exploiters Conservationists Game: how to be an Effective Conservationist -- Analysing the Harvesting Game or why are there so Many Kinds of Fishing Vessels in the Fleet? Permalink : https://genes.bibli.fr/index.php?lvl=notice_display&id=127604 Mathematical Modeling in Ecology / Clark Jeffries / Bâle (CHE) ; Boston, MA : Birkhäuser (1989)
Titre : Mathematical Modeling in Ecology : A Workbook for Students Type de document : document électronique Auteurs : Clark Jeffries ; SpringerLink (Online service) Editeur : Bâle (CHE) ; Boston, MA : Birkhäuser Année de publication : 1989 Collection : Mathematical Modelling num. 3 Importance : X, 194 p Présentation : online resource ISBN/ISSN/EAN : 978-1-4612-4550-6 Langues : Anglais (eng) Tags : Mathematics Earth sciences Applied mathematics Engineering mathematics Mathematical models Mathematical Modeling and Industrial Mathematics Applications of Mathematics Earth Sciences Résumé : Mathematical ecology is the application of mathematics to describe and understand ecosystems. There are two main approaches. One is to describe natural communities and induce statistical patterns or relationships which should generally occur. However, this book is devoted entirely to introducing the student to the second approach: to study deterministic mathematical models and, on the basis of mathematical results on the models, to look for the same patterns or relationships in nature. This book is a compromise between three competing desiderata. It seeks to: maximize the generality of the models; constrain the models to "behave" realistically, that is, to exhibit stability and other features; and minimize the difficulty of presentations of the models. The ultimate goal of the book is to introduce the reader to the general mathematical tools used in building realistic ecosystem models. Just such a model is presented in Chapter Nine. The book should also serve as a stepping-stone both to advanced mathematical works like Stability of Biological Communities by Yu. M. Svirezhev and D. O. Logofet (Mir, Moscow, 1983) and to advanced modeling texts like Freshwater Ecosystems by M. Straskraba and A. H. Gnauch (Elsevier, Amsterdam, 1985) Note de contenu : One-An Introduction to Dynamical Systems as Models -- 1.1 Ecosystem Development in Terms of Ecology -- 1.2 State Space, or How to Add Apples and Oranges -- 1.3 Dynamical Systems as Treasure Hunts -- Two-Simple Difference Equation Models -- 2.1 Predator-Prey Difference Equation Dynamical Systems -- 2.2 Probabilistic Limit Cycles -- Three-Formalizing the Notion of Stability -- 3.1 The Concept of Ecosystem Stability -- 3.2 The Relation of Difference and Differential Equations -- 3.3 Limit Cycles -- 3.4 Lyapunov Theory -- 3.5 The Trapping of Trajectories -- Four-Introduction to Ecosystem Models -- 4.1 Brewing Beer and Yeast Population Dynamics -- 4.2 Attractor Trajectories -- 4.3 Derivatives of System Functions -- 4.4 The Linearization Theorem -- 4.5 The Hurwitz Stability Test -- Five-Introduction to Ecosystem Models -- 5.1 The Community Matrix -- 5.2 Predator-Prey Equations and Generalizations Thereof -- 5.3 Signed Digraphs -- 5.4 Qualitative Stability of Linear Systems -- Six-Qualitative Stability of Ecosystem Models -- 6.1 Qualitative Results in Modeling -- 6.2 Holistic Ecosystem Models -- 6.3 Holistic Ecosystem Models with Attractor Trajectories -- Seven-The Behavior of Models with Attractor Regions -- 7.1 Attractor Regions -- 7.2 The Lorenz Model -- 7.3 Elementary Ecosystem Models with Chaotic Dynamics -- Eight-Holistic Ecosystem Models with Attractor Regions -- 8.1 An Attractor Region Theorem -- 8.2 An Example -- Nine-Sequencing Energy Flow Models to Account for Shortgrass Prairie Energy Dynamics -- 9.1 Energy Flow and Accumulation Modeling -- 9.2 Accumulation Modeling -- 9.3 Estimating Energy Flows -- 9.4 Equations and Trajectories -- 9.5 Stability Permalink : https://genes.bibli.fr/index.php?lvl=notice_display&id=127200 Mathematical Modeling in Ecology : A Workbook for Students [document électronique] / Clark Jeffries ; SpringerLink (Online service) . - Bâle (CHE) ; Boston, MA : Birkhäuser, 1989 . - X, 194 p : online resource. - (Mathematical Modelling; 3) .
ISBN : 978-1-4612-4550-6
Langues : Anglais (eng)
Tags : Mathematics Earth sciences Applied mathematics Engineering mathematics Mathematical models Mathematical Modeling and Industrial Mathematics Applications of Mathematics Earth Sciences Résumé : Mathematical ecology is the application of mathematics to describe and understand ecosystems. There are two main approaches. One is to describe natural communities and induce statistical patterns or relationships which should generally occur. However, this book is devoted entirely to introducing the student to the second approach: to study deterministic mathematical models and, on the basis of mathematical results on the models, to look for the same patterns or relationships in nature. This book is a compromise between three competing desiderata. It seeks to: maximize the generality of the models; constrain the models to "behave" realistically, that is, to exhibit stability and other features; and minimize the difficulty of presentations of the models. The ultimate goal of the book is to introduce the reader to the general mathematical tools used in building realistic ecosystem models. Just such a model is presented in Chapter Nine. The book should also serve as a stepping-stone both to advanced mathematical works like Stability of Biological Communities by Yu. M. Svirezhev and D. O. Logofet (Mir, Moscow, 1983) and to advanced modeling texts like Freshwater Ecosystems by M. Straskraba and A. H. Gnauch (Elsevier, Amsterdam, 1985) Note de contenu : One-An Introduction to Dynamical Systems as Models -- 1.1 Ecosystem Development in Terms of Ecology -- 1.2 State Space, or How to Add Apples and Oranges -- 1.3 Dynamical Systems as Treasure Hunts -- Two-Simple Difference Equation Models -- 2.1 Predator-Prey Difference Equation Dynamical Systems -- 2.2 Probabilistic Limit Cycles -- Three-Formalizing the Notion of Stability -- 3.1 The Concept of Ecosystem Stability -- 3.2 The Relation of Difference and Differential Equations -- 3.3 Limit Cycles -- 3.4 Lyapunov Theory -- 3.5 The Trapping of Trajectories -- Four-Introduction to Ecosystem Models -- 4.1 Brewing Beer and Yeast Population Dynamics -- 4.2 Attractor Trajectories -- 4.3 Derivatives of System Functions -- 4.4 The Linearization Theorem -- 4.5 The Hurwitz Stability Test -- Five-Introduction to Ecosystem Models -- 5.1 The Community Matrix -- 5.2 Predator-Prey Equations and Generalizations Thereof -- 5.3 Signed Digraphs -- 5.4 Qualitative Stability of Linear Systems -- Six-Qualitative Stability of Ecosystem Models -- 6.1 Qualitative Results in Modeling -- 6.2 Holistic Ecosystem Models -- 6.3 Holistic Ecosystem Models with Attractor Trajectories -- Seven-The Behavior of Models with Attractor Regions -- 7.1 Attractor Regions -- 7.2 The Lorenz Model -- 7.3 Elementary Ecosystem Models with Chaotic Dynamics -- Eight-Holistic Ecosystem Models with Attractor Regions -- 8.1 An Attractor Region Theorem -- 8.2 An Example -- Nine-Sequencing Energy Flow Models to Account for Shortgrass Prairie Energy Dynamics -- 9.1 Energy Flow and Accumulation Modeling -- 9.2 Accumulation Modeling -- 9.3 Estimating Energy Flows -- 9.4 Equations and Trajectories -- 9.5 Stability Permalink : https://genes.bibli.fr/index.php?lvl=notice_display&id=127200