Modeling by nonlinear differential equations :: dissipative and conservative processes /
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, react...
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Singapore ; Hackensack, N.J. :
World Scientific Pub. Co.,
©2009.
|
| Schriftenreihe: | World Scientific series on nonlinear science. Monographs and treatises ;
v. 69. |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Zusammenfassung: | 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 resource (xi, 225 pages) : illustrations (some color) |
| Bibliographie: | Includes bibliographical references (pages 213-222) and index. |
| ISBN: | 9789814271608 9814271608 |
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| 245 | 1 | 0 | |a Modeling by nonlinear differential equations : |b dissipative and conservative processes / |c Paul E. Phillipson, Peter Schuster. |
| 260 | |a Singapore ; |a Hackensack, N.J. : |b World Scientific Pub. Co., |c ©2009. | ||
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| 490 | 1 | |a World Scientific series on nonlinear science. Series A ; |v v. 69 | |
| 504 | |a Includes bibliographical references (pages 213-222) and index. | ||
| 505 | 0 | |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. | |
| 520 | |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. | ||
| 588 | 0 | |a Print version record. | |
| 650 | 0 | |a Differential equations, Nonlinear. |0 http://id.loc.gov/authorities/subjects/sh85037906 | |
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| 650 | 0 | |a Mathematical models. |0 http://id.loc.gov/authorities/subjects/sh85082124 | |
| 650 | 6 | |a Équations différentielles non linéaires. | |
| 650 | 6 | |a Équations aux dérivées partielles. | |
| 650 | 6 | |a Modèles mathématiques. | |
| 650 | 7 | |a mathematical models. |2 aat | |
| 650 | 7 | |a MATHEMATICS |x Differential Equations |x General. |2 bisacsh | |
| 650 | 7 | |a Differential equations, Nonlinear |2 fast | |
| 650 | 7 | |a Differential equations, Partial |2 fast | |
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| author | Phillipson, Paul E. (Paul Edgar), 1933- |
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| contents | 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. |
| ctrlnum | (OCoLC)613343558 |
| 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 | Biologie Mathematik |
| format | Electronic eBook |
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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. 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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.</subfield></datafield><datafield tag="588" ind1="0" ind2=" "><subfield code="a">Print version record.</subfield></datafield><datafield tag="650" ind1=" " ind2="0"><subfield code="a">Differential equations, Nonlinear.</subfield><subfield code="0">http://id.loc.gov/authorities/subjects/sh85037906</subfield></datafield><datafield tag="650" ind1=" " ind2="0"><subfield code="a">Differential equations, Partial.</subfield><subfield code="0">http://id.loc.gov/authorities/subjects/sh85037912</subfield></datafield><datafield tag="650" ind1=" " ind2="0"><subfield code="a">Mathematical models.</subfield><subfield code="0">http://id.loc.gov/authorities/subjects/sh85082124</subfield></datafield><datafield tag="650" ind1=" " ind2="6"><subfield code="a">Équations différentielles non linéaires.</subfield></datafield><datafield tag="650" ind1=" " ind2="6"><subfield code="a">Équations aux dérivées partielles.</subfield></datafield><datafield tag="650" ind1=" " ind2="6"><subfield code="a">Modèles mathématiques.</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">mathematical models.</subfield><subfield code="2">aat</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">MATHEMATICS</subfield><subfield code="x">Differential Equations</subfield><subfield code="x">General.</subfield><subfield code="2">bisacsh</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Differential equations, Nonlinear</subfield><subfield code="2">fast</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Differential equations, Partial</subfield><subfield code="2">fast</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Mathematical models</subfield><subfield code="2">fast</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Nichtlineare Differentialgleichung</subfield><subfield code="2">gnd</subfield><subfield code="0">http://d-nb.info/gnd/4205536-2</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Schuster, P.</subfield><subfield code="q">(Peter),</subfield><subfield code="d">1941-</subfield><subfield code="1">https://id.oclc.org/worldcat/entity/E39PBJcgv3cQwHC8KWXgRDkv73</subfield><subfield code="0">http://id.loc.gov/authorities/names/n79018770</subfield></datafield><datafield tag="710" ind1="2" ind2=" "><subfield code="a">World Scientific (Firm)</subfield><subfield code="0">http://id.loc.gov/authorities/names/no2001005546</subfield></datafield><datafield tag="776" ind1="1" ind2=" "><subfield code="z">9814271594</subfield></datafield><datafield tag="776" ind1="1" ind2=" "><subfield code="z">9789814271592</subfield></datafield><datafield tag="830" ind1=" " ind2="0"><subfield code="a">World Scientific series on nonlinear science.</subfield><subfield code="n">Series A,</subfield><subfield code="p">Monographs and treatises ;</subfield><subfield code="v">v. 69.</subfield><subfield code="0">http://id.loc.gov/authorities/names/no94008495</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="l">FWS01</subfield><subfield code="p">ZDB-4-EBA</subfield><subfield code="q">FWS_PDA_EBA</subfield><subfield code="u">https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=340581</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="938" ind1=" " ind2=" "><subfield code="a">Askews and Holts Library Services</subfield><subfield code="b">ASKH</subfield><subfield code="n">AH24686313</subfield></datafield><datafield tag="938" ind1=" " ind2=" "><subfield code="a">ebrary</subfield><subfield code="b">EBRY</subfield><subfield code="n">ebr10421988</subfield></datafield><datafield tag="938" ind1=" " ind2=" "><subfield code="a">EBSCOhost</subfield><subfield code="b">EBSC</subfield><subfield code="n">340581</subfield></datafield><datafield tag="938" ind1=" " ind2=" "><subfield code="a">YBP Library Services</subfield><subfield code="b">YANK</subfield><subfield code="n">3511408</subfield></datafield><datafield tag="994" ind1=" " ind2=" "><subfield code="a">92</subfield><subfield code="b">GEBAY</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">ZDB-4-EBA</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-863</subfield></datafield></record></collection> |
| id | ZDB-4-EBA-ocn613343558 |
| illustrated | Illustrated |
| indexdate | 2024-11-27T13:17:11Z |
| institution | BVB |
| institution_GND | http://id.loc.gov/authorities/names/no2001005546 |
| isbn | 9789814271608 9814271608 |
| language | English |
| lccn | 2012359228 |
| oclc_num | 613343558 |
| open_access_boolean | |
| owner | MAIN DE-863 DE-BY-FWS |
| owner_facet | MAIN DE-863 DE-BY-FWS |
| physical | 1 online resource (xi, 225 pages) : illustrations (some color) |
| psigel | ZDB-4-EBA |
| publishDate | 2009 |
| publishDateSearch | 2009 |
| publishDateSort | 2009 |
| publisher | World Scientific Pub. Co., |
| record_format | marc |
| series | World Scientific series on nonlinear science. Monographs and treatises ; |
| series2 | World Scientific series on nonlinear science. Series A ; |
| spelling | Phillipson, Paul E. (Paul Edgar), 1933- https://id.oclc.org/worldcat/entity/E39PCjFkbFRBFbgjbRGjYfGVhb http://id.loc.gov/authorities/names/no2010016498 Modeling by nonlinear differential equations : dissipative and conservative processes / Paul E. Phillipson, Peter Schuster. Singapore ; Hackensack, N.J. : World Scientific Pub. Co., ©2009. 1 online resource (xi, 225 pages) : illustrations (some color) text txt rdacontent computer c rdamedia online resource cr rdacarrier World Scientific series on nonlinear science. Series A ; v. 69 Includes bibliographical references (pages 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. Print version record. Differential equations, Nonlinear. http://id.loc.gov/authorities/subjects/sh85037906 Differential equations, Partial. http://id.loc.gov/authorities/subjects/sh85037912 Mathematical models. http://id.loc.gov/authorities/subjects/sh85082124 Équations différentielles non linéaires. Équations aux dérivées partielles. Modèles mathématiques. mathematical models. aat MATHEMATICS Differential Equations General. bisacsh Differential equations, Nonlinear fast Differential equations, Partial fast Mathematical models fast Nichtlineare Differentialgleichung gnd http://d-nb.info/gnd/4205536-2 Schuster, P. (Peter), 1941- https://id.oclc.org/worldcat/entity/E39PBJcgv3cQwHC8KWXgRDkv73 http://id.loc.gov/authorities/names/n79018770 World Scientific (Firm) http://id.loc.gov/authorities/names/no2001005546 9814271594 9789814271592 World Scientific series on nonlinear science. Series A, Monographs and treatises ; v. 69. http://id.loc.gov/authorities/names/no94008495 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=340581 Volltext |
| spellingShingle | Phillipson, Paul E. (Paul Edgar), 1933- Modeling by nonlinear differential equations : dissipative and conservative processes / World Scientific series on nonlinear science. Monographs and treatises ; 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. Differential equations, Nonlinear. http://id.loc.gov/authorities/subjects/sh85037906 Differential equations, Partial. http://id.loc.gov/authorities/subjects/sh85037912 Mathematical models. http://id.loc.gov/authorities/subjects/sh85082124 Équations différentielles non linéaires. Équations aux dérivées partielles. Modèles mathématiques. mathematical models. aat MATHEMATICS Differential Equations General. bisacsh Differential equations, Nonlinear fast Differential equations, Partial fast Mathematical models fast Nichtlineare Differentialgleichung gnd http://d-nb.info/gnd/4205536-2 |
| subject_GND | http://id.loc.gov/authorities/subjects/sh85037906 http://id.loc.gov/authorities/subjects/sh85037912 http://id.loc.gov/authorities/subjects/sh85082124 http://d-nb.info/gnd/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 | Differential equations, Nonlinear. http://id.loc.gov/authorities/subjects/sh85037906 Differential equations, Partial. http://id.loc.gov/authorities/subjects/sh85037912 Mathematical models. http://id.loc.gov/authorities/subjects/sh85082124 Équations différentielles non linéaires. Équations aux dérivées partielles. Modèles mathématiques. mathematical models. aat MATHEMATICS Differential Equations General. bisacsh Differential equations, Nonlinear fast Differential equations, Partial fast Mathematical models fast Nichtlineare Differentialgleichung gnd http://d-nb.info/gnd/4205536-2 |
| topic_facet | Differential equations, Nonlinear. Differential equations, Partial. Mathematical models. Équations différentielles non linéaires. Équations aux dérivées partielles. Modèles mathématiques. mathematical models. MATHEMATICS Differential Equations General. Differential equations, Nonlinear Differential equations, Partial Mathematical models Nichtlineare Differentialgleichung |
| url | https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=340581 |
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