Modeling by nonlinear differential equations: dissipative and conservative processes
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Singapore
World Scientific Pub. Co.
c2009
|
| Schriftenreihe: | World Scientific series on nonlinear science
v. 69 |
| Schlagworte: | |
| Online-Zugang: | FAW01 FAW02 Volltext |
| Beschreibung: | Includes bibliographical references (p. 213-222) and index 1. Theme and contents of this book -- 2. Processes in closed and open systems. 2.1. Introduction. 2.2. Thermodynamics of general systems. 2.3. Chemical reactions. 2.4. Autocatalysis in closed and open systems -- 3. Dynamics of molecular evolution. 3.1. Introduction. 3.2. Selection and evolution. 3.3. Template induced autocatalysis. 3.4. Replicator equations. 3.5. Unlimited growth and selection -- 4. Relaxation oscillations. 4.1. Introduction. 4.2. Self-exciting relaxation oscillations. 4.3. Current induced neuron oscillations. 4.4. Bistability and complex structure of harmonically forced relaxation oscillations -- 5. Order and chaos. 5.1. Introduction. 5.2. One dimensional maps. 5.3. Lorenz equations. 5.4. Low dimensional autocatalytic networks. 5.5. Chua equations -- 6. Reaction diffusion dynamics. 6.1. Introduction. 6.2. Pulse front solutions of Fisher and related equations. 6.3. Diffusion driven spatial inhomogeneities. 6.4. Turing mechanism of chemical pattern formation -- 7. Solitons. 7.1. Introduction. 7.2. One dimensional lattice dynamics. 7.3. Burgers equation -- 8. Neuron pulse propagation. 8.1. Introduction. 8.2. Properties of a neural pulse. 8.3. FitzHugh-Nagumo equations. 8.4. Hodgkin-Huxley equations. 8.5. An overview -- 9. Time reversal, dissipation and conservation. 9.1. Introduction. 9.2. Irreversibility and diffusion. 9.3. Reversibility and time recurrence. 9.4. Complex dynamics and chaos in Newtonian dynamics : Hénon-Heiles equations This book aims to provide mathematical analyses of nonlinear differential equations, which have proved pivotal to understanding many phenomena in physics, chemistry and biology. Topics of focus are autocatalysis and dynamics of molecular evolution, relaxation oscillations, deterministic chaos, reaction diffusion driven chemical pattern formation, solitons and neuron dynamics. Included is a discussion of processes from the viewpoints of reversibility, reflected by conservative classical mechanics, and irreversibility introduced by the dissipative role of diffusion. Each chapter presents the subject matter from the point of one or a few key equations, whose properties and consequences are amplified by approximate analytic solutions that are developed to support graphical display of exact computer solutions |
| Beschreibung: | 1 Online-Ressource (xi, 225 p.) |
| ISBN: | 9789814271592 9789814271608 9814271594 9814271608 |
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| 500 | |a 1. Theme and contents of this book -- 2. Processes in closed and open systems. 2.1. Introduction. 2.2. Thermodynamics of general systems. 2.3. Chemical reactions. 2.4. Autocatalysis in closed and open systems -- 3. Dynamics of molecular evolution. 3.1. Introduction. 3.2. Selection and evolution. 3.3. Template induced autocatalysis. 3.4. Replicator equations. 3.5. Unlimited growth and selection -- 4. Relaxation oscillations. 4.1. Introduction. 4.2. Self-exciting relaxation oscillations. 4.3. Current induced neuron oscillations. 4.4. Bistability and complex structure of harmonically forced relaxation oscillations -- 5. Order and chaos. 5.1. Introduction. 5.2. One dimensional maps. 5.3. Lorenz equations. 5.4. Low dimensional autocatalytic networks. 5.5. Chua equations -- 6. Reaction diffusion dynamics. 6.1. Introduction. 6.2. Pulse front solutions of Fisher and related equations. 6.3. Diffusion driven spatial inhomogeneities. 6.4. Turing mechanism of chemical pattern formation -- 7. Solitons. 7.1. Introduction. 7.2. One dimensional lattice dynamics. 7.3. Burgers equation -- 8. Neuron pulse propagation. 8.1. Introduction. 8.2. Properties of a neural pulse. 8.3. FitzHugh-Nagumo equations. 8.4. Hodgkin-Huxley equations. 8.5. An overview -- 9. Time reversal, dissipation and conservation. 9.1. Introduction. 9.2. Irreversibility and diffusion. 9.3. Reversibility and time recurrence. 9.4. Complex dynamics and chaos in Newtonian dynamics : Hénon-Heiles equations | ||
| 500 | |a This book aims to provide mathematical analyses of nonlinear differential equations, which have proved pivotal to understanding many phenomena in physics, chemistry and biology. Topics of focus are autocatalysis and dynamics of molecular evolution, relaxation oscillations, deterministic chaos, reaction diffusion driven chemical pattern formation, solitons and neuron dynamics. Included is a discussion of processes from the viewpoints of reversibility, reflected by conservative classical mechanics, and irreversibility introduced by the dissipative role of diffusion. Each chapter presents the subject matter from the point of one or a few key equations, whose properties and consequences are amplified by approximate analytic solutions that are developed to support graphical display of exact computer solutions | ||
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Datensatz im Suchindex
| _version_ | 1804175601348640768 |
|---|---|
| any_adam_object | |
| author | Phillipson, Paul E. 1933- |
| author_GND | (DE-588)139376461 (DE-588)132500965 |
| author_facet | Phillipson, Paul E. 1933- |
| author_role | aut |
| author_sort | Phillipson, Paul E. 1933- |
| author_variant | p e p pe pep |
| building | Verbundindex |
| bvnumber | BV043146531 |
| collection | ZDB-4-EBA |
| ctrlnum | (OCoLC)613343558 (DE-599)BVBBV043146531 |
| dewey-full | 515.35 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515.35 |
| dewey-search | 515.35 |
| dewey-sort | 3515.35 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Electronic eBook |
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| id | DE-604.BV043146531 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:18:53Z |
| institution | BVB |
| isbn | 9789814271592 9789814271608 9814271594 9814271608 |
| language | English |
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| physical | 1 Online-Ressource (xi, 225 p.) |
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| publishDate | 2009 |
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| series2 | World Scientific series on nonlinear science |
| spelling | Phillipson, Paul E. 1933- Verfasser (DE-588)139376461 aut Modeling by nonlinear differential equations dissipative and conservative processes Paul E. Phillipson, Peter Schuster Singapore World Scientific Pub. Co. c2009 1 Online-Ressource (xi, 225 p.) txt rdacontent c rdamedia cr rdacarrier World Scientific series on nonlinear science v. 69 Includes bibliographical references (p. 213-222) and index 1. Theme and contents of this book -- 2. Processes in closed and open systems. 2.1. Introduction. 2.2. Thermodynamics of general systems. 2.3. Chemical reactions. 2.4. Autocatalysis in closed and open systems -- 3. Dynamics of molecular evolution. 3.1. Introduction. 3.2. Selection and evolution. 3.3. Template induced autocatalysis. 3.4. Replicator equations. 3.5. Unlimited growth and selection -- 4. Relaxation oscillations. 4.1. Introduction. 4.2. Self-exciting relaxation oscillations. 4.3. Current induced neuron oscillations. 4.4. Bistability and complex structure of harmonically forced relaxation oscillations -- 5. Order and chaos. 5.1. Introduction. 5.2. One dimensional maps. 5.3. Lorenz equations. 5.4. Low dimensional autocatalytic networks. 5.5. Chua equations -- 6. Reaction diffusion dynamics. 6.1. Introduction. 6.2. Pulse front solutions of Fisher and related equations. 6.3. Diffusion driven spatial inhomogeneities. 6.4. Turing mechanism of chemical pattern formation -- 7. Solitons. 7.1. Introduction. 7.2. One dimensional lattice dynamics. 7.3. Burgers equation -- 8. Neuron pulse propagation. 8.1. Introduction. 8.2. Properties of a neural pulse. 8.3. FitzHugh-Nagumo equations. 8.4. Hodgkin-Huxley equations. 8.5. An overview -- 9. Time reversal, dissipation and conservation. 9.1. Introduction. 9.2. Irreversibility and diffusion. 9.3. Reversibility and time recurrence. 9.4. Complex dynamics and chaos in Newtonian dynamics : Hénon-Heiles equations This book aims to provide mathematical analyses of nonlinear differential equations, which have proved pivotal to understanding many phenomena in physics, chemistry and biology. Topics of focus are autocatalysis and dynamics of molecular evolution, relaxation oscillations, deterministic chaos, reaction diffusion driven chemical pattern formation, solitons and neuron dynamics. Included is a discussion of processes from the viewpoints of reversibility, reflected by conservative classical mechanics, and irreversibility introduced by the dissipative role of diffusion. Each chapter presents the subject matter from the point of one or a few key equations, whose properties and consequences are amplified by approximate analytic solutions that are developed to support graphical display of exact computer solutions MATHEMATICS / Differential Equations / General bisacsh Nichtlineare Differentialgleichung swd Mathematisches Modell Differential equations, Nonlinear Differential equations, Partial Mathematical models Nichtlineare Differentialgleichung (DE-588)4205536-2 gnd rswk-swf Nichtlineare Differentialgleichung (DE-588)4205536-2 s 1\p DE-604 Schuster, Peter 1941- Sonstige (DE-588)132500965 oth World Scientific (Firm) Sonstige oth http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=340581 Aggregator Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Phillipson, Paul E. 1933- Modeling by nonlinear differential equations dissipative and conservative processes MATHEMATICS / Differential Equations / General bisacsh Nichtlineare Differentialgleichung swd Mathematisches Modell Differential equations, Nonlinear Differential equations, Partial Mathematical models Nichtlineare Differentialgleichung (DE-588)4205536-2 gnd |
| subject_GND | (DE-588)4205536-2 |
| title | Modeling by nonlinear differential equations dissipative and conservative processes |
| title_auth | Modeling by nonlinear differential equations dissipative and conservative processes |
| title_exact_search | Modeling by nonlinear differential equations dissipative and conservative processes |
| title_full | Modeling by nonlinear differential equations dissipative and conservative processes Paul E. Phillipson, Peter Schuster |
| title_fullStr | Modeling by nonlinear differential equations dissipative and conservative processes Paul E. Phillipson, Peter Schuster |
| title_full_unstemmed | Modeling by nonlinear differential equations dissipative and conservative processes Paul E. Phillipson, Peter Schuster |
| title_short | Modeling by nonlinear differential equations |
| title_sort | modeling by nonlinear differential equations dissipative and conservative processes |
| title_sub | dissipative and conservative processes |
| topic | MATHEMATICS / Differential Equations / General bisacsh Nichtlineare Differentialgleichung swd Mathematisches Modell Differential equations, Nonlinear Differential equations, Partial Mathematical models Nichtlineare Differentialgleichung (DE-588)4205536-2 gnd |
| topic_facet | MATHEMATICS / Differential Equations / General Nichtlineare Differentialgleichung Mathematisches Modell Differential equations, Nonlinear Differential equations, Partial Mathematical models |
| url | http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=340581 |
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