Modeling by nonlinear differential equations: dissipative and conservative processes
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New Jersey [u.a.]
World Scientific
2009
|
| Series: | World Scientific series on nonlinear science
Series A, Monographs and treatises ; 69 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XI, 225 S. Ill., graph. Darst. |
| ISBN: | 9789814271592 9814271594 |
Staff View
MARC
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| 020 | |a 9814271594 |9 981-4271-59-4 | ||
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| 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 |
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Record in the Search Index
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|---|---|
| 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
|
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| dewey-tens | 510 - Mathematics |
| discipline | Biologie Mathematik |
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| id | DE-604.BV035754942 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T22:03:45Z |
| institution | BVB |
| isbn | 9789814271592 9814271594 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-018614926 |
| oclc_num | 298782396 |
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| 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 |
| spelling | Phillipson, Paul E. 1933- Verfasser (DE-588)139376461 aut Modeling by nonlinear differential equations dissipative and conservative processes Paul E. Phillipson ; Peter Schuster New Jersey [u.a.] World Scientific 2009 XI, 225 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier World Scientific series on nonlinear science : Series A, Monographs and treatises 69 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 DE-604 Schuster, Peter 1941- Verfasser (DE-588)132500965 aut World Scientific series on nonlinear science Series A, Monographs and treatises ; 69 (DE-604)BV009051753 69 Digitalisierung UB Regensburg application/pdf 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 Inhaltsverzeichnis |
| 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 |
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