Modeling by nonlinear differential equations: dissipative and conservative processes
Gespeichert in:
| Beteiligte Personen: | , |
|---|---|
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
New Jersey [u.a.]
World Scientific
2009
|
| Schriftenreihe: | World Scientific series on nonlinear science
Series A, Monographs and treatises ; 69 |
| Schlagwörter: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018614926&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Umfang: | XI, 225 S. Ill., graph. Darst. |
| ISBN: | 9789814271592 9814271594 |
Internformat
MARC
| LEADER | 00000nam a2200000 cb4500 | ||
|---|---|---|---|
| 001 | BV035754942 | ||
| 003 | DE-604 | ||
| 005 | 20130306 | ||
| 007 | t| | ||
| 008 | 091006s2009 xx ad|| |||| 00||| eng d | ||
| 020 | |a 9789814271592 |9 978-981-4271-59-2 | ||
| 020 | |a 9814271594 |9 981-4271-59-4 | ||
| 035 | |a (OCoLC)298782396 | ||
| 035 | |a (DE-599)BVBBV035754942 | ||
| 040 | |a DE-604 |b ger |e rakwb | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-355 |a DE-384 |a DE-11 |a DE-824 |a DE-703 | ||
| 050 | 0 | |a QA372 | |
| 082 | 0 | |a 515.35 | |
| 084 | |a SK 520 |0 (DE-625)143244: |2 rvk | ||
| 084 | |a WD 2100 |0 (DE-625)148162: |2 rvk | ||
| 100 | 1 | |a Phillipson, Paul E. |d 1933- |e Verfasser |0 (DE-588)139376461 |4 aut | |
| 245 | 1 | 0 | |a Modeling by nonlinear differential equations |b dissipative and conservative processes |c Paul E. Phillipson ; Peter Schuster |
| 264 | 1 | |a New Jersey [u.a.] |b World Scientific |c 2009 | |
| 300 | |a XI, 225 S. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a World Scientific series on nonlinear science : Series A, Monographs and treatises |v 69 | |
| 650 | 4 | |a Mathematisches Modell | |
| 650 | 4 | |a Differential equations, Nonlinear | |
| 650 | 4 | |a Differential equations, Partial | |
| 650 | 4 | |a Mathematical models | |
| 650 | 0 | 7 | |a Nichtlineare Differentialgleichung |0 (DE-588)4205536-2 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Nichtlineare Differentialgleichung |0 (DE-588)4205536-2 |D s |
| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Schuster, Peter |d 1941- |e Verfasser |0 (DE-588)132500965 |4 aut | |
| 830 | 0 | |a World Scientific series on nonlinear science |v Series A, Monographs and treatises ; 69 |w (DE-604)BV009051753 |9 69 | |
| 856 | 4 | 2 | |m Digitalisierung UB Regensburg |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018614926&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-018614926 | |
Datensatz im Suchindex
| _version_ | 1819376826403782656 |
|---|---|
| adam_text | Contents
Acknowledgments
xi
1.
Theme and Contents of this Book
1
2.
Processes in Closed and Open Systems
9
2.1
Introduction
........................ 9
2.2
Thermodynamics of general systems
........... 10
2.3
Chemical reactions
.................... 12
2.4
Autocatalysis in closed and open systems
........ 18
2.4.1
Autocatalysis in closed systems
......... 19
2.4.2
Autocatalysis in the flow reactor
........ 21
3.
Dynamics of Molecular Evolution
29
3.1
Introduction
........................ 29
3.2
Selection and evolution
.................. 30
3.3
Template induced autocatalysis
............. 33
3.3.1
Autocatalytic oligomerization
.......... 34
3.3.2 Biopolymer
replication
.............. 38
3.3.3
Replication and selection
............ 46
3.3.4
Replication and mutation
............ 51
3.3.5
Error thresholds
................. 57
3.4
Replicator equations
................... 61
3.4.1 Schlögl
model
................... 65
3.4.2
Fisher s selection equation
............ 67
3.4.3
Symbioses
and hypercycles
........... 70
3.5
Unlimited growth and selection
............. 74
viii
Modeling by Nonlinear Differential Equations
4.
Relaxation Oscillations
77
4.1
Introduction
........................77
4.2
Self-exciting relaxation oscillations
...........78
4.2.1
van
der Pol
equation
.............. 78
4.2.2
Stoker-Haag
equation
.............. 83
4.3
Current induced neuron oscillations
........... 87
4.4
Bistability and complex structure of harmonically
forced relaxation oscillations
............... 92
5.
Order and Chaos
101
5.1
Introduction
........................101
5.2
One dimensional maps
..................102
5.2.1
Formation of a period window
.........105
5.2.2
Stability of a period window
..........108
5.2.3
Topology of one dimensional maps
.......109
5.3 Lorenz
equations
.....................
Ill
5.4
Low dimensional autocatalytic networks
........117
5.5
Chua equations
......................121
6.
Reaction Diffusion Dynamics
123
6.1
Introduction
........................123
6.2
Pulse front solutions of Fisher and related equations
. . 124
6.3
Diffusion driven spatial inhomogeneities
.........128
6.4
Turing mechanism of chemical pattern formation
. . . 133
7. Solitons 143
7.1
Introduction
........................143
7.2
One dimensional lattice dynamics
............144
7.2.1
Korteweg-de
Vries
equation
...........149
7.2.2
sine-Gordon equation
..............155
7.3
Burgers equation
.....................161
8.
Neuron Pulse Propagation
165
8.1
Introduction
........................165
8.2
Properties of a neural pulse
...............166
8.3
FitzHugh-Nagumo equations
...............168
Contents ix
8.4 Hodgkin-Huxley
equations................
173
8.5 An
overview .......................
181
9.
Time Reversal, Dissipation and Conservation
183
9.1
Introduction
........................183
9.2
Irreversibility and diffusion
................185
9.2.1
Theory of random walk
.............185
9.2.2
Langevin
equation and equilibrium fluctuations
187
9.2.3
Newtonian mechanics and asymptotic
irreversibility
...................189
9.3
Reversibility and time recurrence
............194
9.3.1
A linear synchronous system
..........195
9.3.2
Recurrence in nonlinear Hamiltonian systems:
Fermi-Pasta-Ulam Model
............198
9.4
Complex dynamics and chaos in Newtonian dynamics:
Hénon-Heiles
equations
..................203
Bibliography
213
Index
223
|
| any_adam_object | 1 |
| author | Phillipson, Paul E. 1933- Schuster, Peter 1941- |
| author_GND | (DE-588)139376461 (DE-588)132500965 |
| author_facet | Phillipson, Paul E. 1933- Schuster, Peter 1941- |
| author_role | aut aut |
| author_sort | Phillipson, Paul E. 1933- |
| author_variant | p e p pe pep p s ps |
| building | Verbundindex |
| bvnumber | BV035754942 |
| callnumber-first | Q - Science |
| callnumber-label | QA372 |
| callnumber-raw | QA372 |
| callnumber-search | QA372 |
| callnumber-sort | QA 3372 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 520 WD 2100 |
| ctrlnum | (OCoLC)298782396 (DE-599)BVBBV035754942 |
| 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 | Book |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01952nam a2200445 cb4500</leader><controlfield tag="001">BV035754942</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20130306 </controlfield><controlfield tag="007">t|</controlfield><controlfield tag="008">091006s2009 xx ad|| |||| 00||| eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9789814271592</subfield><subfield code="9">978-981-4271-59-2</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9814271594</subfield><subfield code="9">981-4271-59-4</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)298782396</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV035754942</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">rakwb</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-355</subfield><subfield code="a">DE-384</subfield><subfield code="a">DE-11</subfield><subfield code="a">DE-824</subfield><subfield code="a">DE-703</subfield></datafield><datafield tag="050" ind1=" " ind2="0"><subfield code="a">QA372</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">515.35</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 520</subfield><subfield code="0">(DE-625)143244:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">WD 2100</subfield><subfield code="0">(DE-625)148162:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Phillipson, Paul E.</subfield><subfield code="d">1933-</subfield><subfield code="e">Verfasser</subfield><subfield code="0">(DE-588)139376461</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Modeling by nonlinear differential equations</subfield><subfield code="b">dissipative and conservative processes</subfield><subfield code="c">Paul E. Phillipson ; Peter Schuster</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">New Jersey [u.a.]</subfield><subfield code="b">World Scientific</subfield><subfield code="c">2009</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">XI, 225 S.</subfield><subfield code="b">Ill., graph. Darst.</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="490" ind1="1" ind2=" "><subfield code="a">World Scientific series on nonlinear science : Series A, Monographs and treatises</subfield><subfield code="v">69</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Mathematisches Modell</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Differential equations, Nonlinear</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Differential equations, Partial</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Mathematical models</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Nichtlineare Differentialgleichung</subfield><subfield code="0">(DE-588)4205536-2</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Nichtlineare Differentialgleichung</subfield><subfield code="0">(DE-588)4205536-2</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Schuster, Peter</subfield><subfield code="d">1941-</subfield><subfield code="e">Verfasser</subfield><subfield code="0">(DE-588)132500965</subfield><subfield code="4">aut</subfield></datafield><datafield tag="830" ind1=" " ind2="0"><subfield code="a">World Scientific series on nonlinear science</subfield><subfield code="v">Series A, Monographs and treatises ; 69</subfield><subfield code="w">(DE-604)BV009051753</subfield><subfield code="9">69</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">Digitalisierung UB Regensburg</subfield><subfield code="q">application/pdf</subfield><subfield code="u">http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018614926&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA</subfield><subfield code="3">Inhaltsverzeichnis</subfield></datafield><datafield tag="943" ind1="1" ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-018614926</subfield></datafield></record></collection> |
| id | DE-604.BV035754942 |
| illustrated | Illustrated |
| indexdate | 2024-12-20T13:59:26Z |
| institution | BVB |
| isbn | 9789814271592 9814271594 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-018614926 |
| oclc_num | 298782396 |
| open_access_boolean | |
| owner | DE-355 DE-BY-UBR DE-384 DE-11 DE-824 DE-703 |
| owner_facet | DE-355 DE-BY-UBR DE-384 DE-11 DE-824 DE-703 |
| physical | XI, 225 S. Ill., graph. Darst. |
| publishDate | 2009 |
| publishDateSearch | 2009 |
| publishDateSort | 2009 |
| publisher | World Scientific |
| record_format | marc |
| series | World Scientific series on nonlinear science |
| series2 | World Scientific series on nonlinear science : Series A, Monographs and treatises |
| spellingShingle | Phillipson, Paul E. 1933- Schuster, Peter 1941- Modeling by nonlinear differential equations dissipative and conservative processes World Scientific series on nonlinear science 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 | Mathematisches Modell Differential equations, Nonlinear Differential equations, Partial Mathematical models Nichtlineare Differentialgleichung (DE-588)4205536-2 gnd |
| topic_facet | Mathematisches Modell Differential equations, Nonlinear Differential equations, Partial Mathematical models Nichtlineare Differentialgleichung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018614926&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV009051753 |
| work_keys_str_mv | AT phillipsonpaule modelingbynonlineardifferentialequationsdissipativeandconservativeprocesses AT schusterpeter modelingbynonlineardifferentialequationsdissipativeandconservativeprocesses |