Introduction to nonlinear science:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cambridge
Cambridge Univ. Press
1995
|
| Edition: | 1. publ. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XV, 254 S. Ill., graph. Darst. |
| ISBN: | 0521467829 0521462282 |
Staff View
MARC
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| 245 | 1 | 0 | |a Introduction to nonlinear science |c G. Nicolis |
| 250 | |a 1. publ. | ||
| 264 | 1 | |a Cambridge |b Cambridge Univ. Press |c 1995 | |
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Record in the Search Index
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|---|---|
| adam_text | Contents
Preface xiii
1 Nonlinear behavior in the physical sciences and biology: some
typical examples.
1.1 What is nonlinearity? 1
1.2 Nonlinear behavior in classical mechanics 2
1.3 Thermal convection 5
1.4 Nonlinear phenomena in chemistry 12
1.5 Some further examples of chemically mediated nonlinear
behavior 19
Problems 23
2 Quantitative formulation
2.1 Evolution equations in classical mechanics 25
2.2 The macroscopic level: balance equation of a
macrovariable 29
2.3 Conserved variables in a one component system and the
equations of fluid dynamics 30
2.4 Nonconserved variables in a multicomponent system and
the equations of chemical kinetics 33
2.5 The Benard problem: quantitative formulation 35
2.6 Some representative chemical models giving
rise to nonlinear behavior 40
Problems 45
3 Dynamical systems with a finite number of degrees
of freedom
3.1 General orientation 47
3.2 Phase space 49
ix
x Contents
3.3 Invariant manifolds 51
3.4 Conservative and dissipative systems. Attractors 58
3.5 Stability 61
3.6 The principle of linearized stability 66
Problems 69
4 Linear stability analysis of fixed points
4.1 General formulation 71
4.2 Systems involving one variable 75
4.3 Systems involving two variables 77
4.4 Examples of stability analysis of two dimensional
dynamical systems 84
4.5 Three variables and beyond 87
Problems 92
5 Nonlinear behavior around fixed points: bifurcation
analysis
5.1 Introduction 94
5.2 Expansion of the solutions in perturbation series: the case
of zero eigenvalue, Re a Q = Im coc = 0 96
5.3 The amplitude equation: transcritical bifurcation 98
5.4 The amplitude equation: pitchfork bifurcation 102
5.5 Limit point bifurcation 104
5.6 Kinetic potential, sensitivity, structural stability 105
5.7 The Hopf bifurcation 110
5.8 Cascading bifurcations 114
5.9 Normal forms and resonances 120
Problems 125
6 Spatially distributed systems, broken symmetries,
pattern formation
6.1 General formulation 128
6.2 The Benard problem: reference state and linearization of
the Boussinesq equations 129
6.3 The Benard problem: linear stability analysis for free
boundaries 133
6.4 Reaction diffusion systems. The Turing instability 138
6.5 Further comments on linear stability in spatially
distributed systems 146
6.6 Bifurcation analysis: general formulation 148
6.7 Bifurcation of two dimensional rolls in the Benard
problem: the small aspect ratio case 151
Contents xi
6.8 Bifurcation analysis in systems of large spatial extent:
complex Landau Ginzburg equation 156
6.9 Further examples of normal form envelope equations in
large systems 161
Problems 169
7 Chaotic dynamics
7.1 The Poincare map 173
7.2 One dimensional recurrences: general aspects 178
7.3 Phenomenology of one dimensional recurrences:
illustrations 180
7.4 Tools of chaos theory 188
7.5 Routes to chaos: quantitative formulation 192
7.6 Fully developed chaos: probabilistic description 196
7.7 Error growth, Lyapunov exponents and predictability 205
7.8 The dynamics of symbolic sequences: entropy, master
equation 211
7.9 Spatio temporal chaos 220
Problems 227
Appendices
Al Proof of the principle of linearized stability for one variable
systems 230
A2 Hopf bifurcation analysis of the Brusselator
model 234
References 239
Index 251
|
| any_adam_object | 1 |
| author | Nicolis, Grégoire 1939-2018 |
| author_GND | (DE-588)172284880 |
| author_facet | Nicolis, Grégoire 1939-2018 |
| author_role | aut |
| author_sort | Nicolis, Grégoire 1939-2018 |
| author_variant | g n gn |
| building | Verbundindex |
| bvnumber | BV010431590 |
| classification_rvk | SK 950 SK 960 UG 3900 |
| classification_tum | MAT 344f |
| ctrlnum | (OCoLC)246740788 (DE-599)BVBBV010431590 |
| dewey-full | 500 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 500 - Natural sciences and mathematics |
| dewey-raw | 500 |
| dewey-search | 500 |
| dewey-sort | 3500 |
| dewey-tens | 500 - Natural sciences and mathematics |
| discipline | Allgemeine Naturwissenschaft Physik Mathematik |
| edition | 1. publ. |
| format | Book |
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| id | DE-604.BV010431590 |
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| indexdate | 2024-07-09T17:52:26Z |
| institution | BVB |
| isbn | 0521467829 0521462282 |
| language | English |
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| physical | XV, 254 S. Ill., graph. Darst. |
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| publisher | Cambridge Univ. Press |
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| spelling | Nicolis, Grégoire 1939-2018 Verfasser (DE-588)172284880 aut Introduction to nonlinear science G. Nicolis 1. publ. Cambridge Cambridge Univ. Press 1995 XV, 254 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Dynamisches System - Nichtlineares Phänomen Nichtlineares System Nichtlineares Phänomen (DE-588)4136065-5 gnd rswk-swf Chaotisches System (DE-588)4316104-2 gnd rswk-swf Mathematische Physik (DE-588)4037952-8 gnd rswk-swf Nichtlineare Theorie (DE-588)4251279-7 gnd rswk-swf Naturwissenschaften (DE-588)4041421-8 gnd rswk-swf Nichtlineares dynamisches System (DE-588)4126142-2 gnd rswk-swf Nichtlineare Theorie (DE-588)4251279-7 s Mathematische Physik (DE-588)4037952-8 s DE-604 Nichtlineares Phänomen (DE-588)4136065-5 s Naturwissenschaften (DE-588)4041421-8 s Nichtlineares dynamisches System (DE-588)4126142-2 s Chaotisches System (DE-588)4316104-2 s 1\p DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006951425&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Nicolis, Grégoire 1939-2018 Introduction to nonlinear science Dynamisches System - Nichtlineares Phänomen Nichtlineares System Nichtlineares Phänomen (DE-588)4136065-5 gnd Chaotisches System (DE-588)4316104-2 gnd Mathematische Physik (DE-588)4037952-8 gnd Nichtlineare Theorie (DE-588)4251279-7 gnd Naturwissenschaften (DE-588)4041421-8 gnd Nichtlineares dynamisches System (DE-588)4126142-2 gnd |
| subject_GND | (DE-588)4136065-5 (DE-588)4316104-2 (DE-588)4037952-8 (DE-588)4251279-7 (DE-588)4041421-8 (DE-588)4126142-2 |
| title | Introduction to nonlinear science |
| title_auth | Introduction to nonlinear science |
| title_exact_search | Introduction to nonlinear science |
| title_full | Introduction to nonlinear science G. Nicolis |
| title_fullStr | Introduction to nonlinear science G. Nicolis |
| title_full_unstemmed | Introduction to nonlinear science G. Nicolis |
| title_short | Introduction to nonlinear science |
| title_sort | introduction to nonlinear science |
| topic | Dynamisches System - Nichtlineares Phänomen Nichtlineares System Nichtlineares Phänomen (DE-588)4136065-5 gnd Chaotisches System (DE-588)4316104-2 gnd Mathematische Physik (DE-588)4037952-8 gnd Nichtlineare Theorie (DE-588)4251279-7 gnd Naturwissenschaften (DE-588)4041421-8 gnd Nichtlineares dynamisches System (DE-588)4126142-2 gnd |
| topic_facet | Dynamisches System - Nichtlineares Phänomen Nichtlineares System Nichtlineares Phänomen Chaotisches System Mathematische Physik Nichtlineare Theorie Naturwissenschaften Nichtlineares dynamisches System |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006951425&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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