Nonlinearity, chaos, and complexity: the dynamics of natural and social systems
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English Italian |
| Published: |
Oxford [u.a.]
Oxford Univ. Press
2005
|
| Edition: | 1. publ. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Includes bibliographical references and indexes. - Formerly CIP |
| Physical Description: | XV, 387 S. graph. Darst. |
| ISBN: | 0198567901 019856791X 9780198567912 |
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| 240 | 1 | 0 | |a Nonlinearità, caos, complessità |
| 245 | 1 | 0 | |a Nonlinearity, chaos, and complexity |b the dynamics of natural and social systems |c Cristoforo Sergio Bertuglia ; Franco Vaio |
| 250 | |a 1. publ. | ||
| 264 | 1 | |a Oxford [u.a.] |b Oxford Univ. Press |c 2005 | |
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Record in the Search Index
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| adam_text | Contents
PART 1 Linear and Nonlinear Processes 1
1 Introduction 3
What we mean by system 3
Physicalism: the first attempt to describe social systems
using the methods of natural systems 5
2 Modelling 10
A brief introduction to modelling 10
Direct problems and inverse problems in modelling 12
The meaning and the value of models 14
3 The origins of system dynamics: mechanics 19
The classical interpretation of mechanics 19
The many body problem and the limitations of classical mechanics 22
4 Linearity in models 27
5 One of the most basic natural systems: the pendulum 32
The linear model (Model 1) 32
The linear model of a pendulum in the presence of friction (Model 2) 35
Autonomous systems 37
6 Linearity as a first, often insufficient approximation 39
The linearization of problems 39
The limitations of linear models 42
7 The nonlinearity of natural processes: the case of the pendulum 46
The nonlinear pendulum (Model 3 without friction, and Model 3
with friction) 46
Non integrability, in general, of nonlinear equations 47
8 Dynamical systems and the phase space 49
What we mean by dynamical system 49
The phase space 50
Oscillatory dynamics represented in the phase space 54
Contents
9 Extension of the concepts and models used in physics to economics 60
Jevons, Pareto and Fisher: from mathematical physics to
mathematical economics 60
Schumpeter and Samuelson: the economic cycle 62
Dow and Elliott: periodicity in financial markets 64
10 The chaotic pendulum 67
The need for models of nonlinear oscillations 67
The case of a nonlinear forced pendulum with friction (Model 4) 68
11 Linear models in social processes: the case of two interacting
populations 71
Introduction 71
The linear model of two interacting populations 72
Some qualitative aspects of linear model dynamics 73
The solutions of the linear model 76
Complex conjugate roots of the characteristic equation: the
values of the two populations fluctuate 84
12 Nonlinear models in social processes: the model of
Volterra Lotka and some of its variants in ecology 93
Introduction 93
The basic model 94
A non punctiform attractor: the limit cycle 98
Carrying capacity 101
Functional response and numerical response of the predator 103
13 Nonlinear models in social processes: the Volterra Lotka
model applied to urban and regional science 108
Introduction 108
Model of joint population income dynamics 108
The population income model applied to US cities and to Madrid 113
The symmetrical competition model and the formation of niches 118
PART 2 From Nonlinearity to Chaos 123
14 Introduction 125
15 Dynamical systems and chaos 127
Some theoretical aspects 127
Two examples: calculating linear and chaotic dynamics 131
Contents
The deterministic vision and real chaotic systems 135
The question of the stability of the solar system 137
16 Strange and chaotic attractors 141
Some preliminary concepts 141
Two examples: Lorenz and Rossler attractors 146
A two dimensional chaotic map: the baker s map 150
17 Chaos in real systems and in mathematical models 154
18 Stability in dynamical systems 159
The concept of stability 159
A basic case: the stability of a linear dynamical system 161
Poincare and Lyapunov stability criteria 163
Application of Lyapunov s criterion to Malthus exponential
law of growth 168
Quantifying a system s instability: the Lyapunov exponents 171
Exponential growth of the perturbations and the predictability
horizon of a model 176
19 The problem of measuring chaos in real systems 179
Chaotic dynamics and stochastic dynamics 179
A method to obtain the dimension of attractors 183
An observation on determinism in economics 186
20 Logistic growth as a population development model 190
Introduction: modelling the growth of a population 190
Growth in the presence of limited resources: Verhulst equation 191
The logistic function 194
21 A nonlinear discrete model: the logistic map 199
Introduction 199
The iteration method and the fixed points of a function 201
The dynamics of the logistic map 204
22 The logistic map: some results of numerical simulations
and an application 214
The Feigenbaum tree 214
An example of the application of the logistic map to
spatial interaction models 224
23 Chaos in systems: the main concepts 231
Contents
PART 3 Complexity 237
24 Introduction 239
25 Inadequacy of reductionism 240
Models as portrayals of reality 240
Reductionism and linearity 241
A reflection on the role of mathematics in models 243
A reflection on mathematics as a tool for modelling 246
The search for regularities in social science phenomena 249
26 Some aspects of the classical vision of science 253
Determinism 253
The principle of sufficient reason 257
The classical vision in social sciences 259
Characteristics of systems described by classical science 261
27 From determinism to complexity: self organization, a new
understanding of system dynamics 266
Introduction 266
The new conceptions of complexity 268
Self organization 271
28 What is complexity? 275
Adaptive complex systems 275
Basic aspects of complexity 277
An observation on complexity in social systems 280
Some attempts at defining a complex system 281
The complexity of a system and the observer 285
The complexity of a system and the relations between its parts 286
29 Complexity and evolution 291
Introduction 291
The three ways in which complexity grows according
to Brian Arthur 291
The Tierra evolutionistic model 295
The appearance of life according to Kauffman 297
30 Complexity in economic processes 301
Complex economic systems 301
Synergetics 304
Two examples of complex models in economics 307
A model of the complex phenomenology of the financial markets 309
Contents
31 Some thoughts on the meaning of doing mathematics 315
The problem of formalizing complexity 315
Mathematics as a useful tool to highlight and express
recurrences 320
A reflection on the efficacy of mathematics as a tool to
describe the world 323
32 Digression into the main interpretations of the foundations
of mathematics 329
Introduction 329
Platonism 330
Formalism and les Bourbaki 331
Constructivism 336
Experimental mathematics 340
The paradigm of the cosmic computer in the vision of
experimental mathematics 341
A comparison between Platonism, formalism, and constructivism
in mathematics 343
33 The need for a mathematics of (or for) complexity 348
The problem of formulating mathematical laws for complexity 348
The description of complexity linked to a better
understanding of the concept of mathematical infinity:
some reflections 351
References 356
Subject index 375
Name index 380
|
| adam_txt |
Contents
PART 1 Linear and Nonlinear Processes 1
1 Introduction 3
What we mean by 'system' 3
Physicalism: the first attempt to describe social systems
using the methods of natural systems 5
2 Modelling 10
A brief introduction to modelling 10
Direct problems and inverse problems in modelling 12
The meaning and the value of models 14
3 The origins of system dynamics: mechanics 19
The classical interpretation of mechanics 19
The many body problem and the limitations of classical mechanics 22
4 Linearity in models 27
5 One of the most basic natural systems: the pendulum 32
The linear model (Model 1) 32
The linear model of a pendulum in the presence of friction (Model 2) 35
Autonomous systems 37
6 Linearity as a first, often insufficient approximation 39
The linearization of problems 39
The limitations of linear models 42
7 The nonlinearity of natural processes: the case of the pendulum 46
The nonlinear pendulum (Model 3 without friction, and Model 3'
with friction) 46
Non integrability, in general, of nonlinear equations 47
8 Dynamical systems and the phase space 49
What we mean by dynamical system 49
The phase space 50
Oscillatory dynamics represented in the phase space 54
Contents
9 Extension of the concepts and models used in physics to economics 60
Jevons, Pareto and Fisher: from mathematical physics to
mathematical economics 60
Schumpeter and Samuelson: the economic cycle 62
Dow and Elliott: periodicity in financial markets 64
10 The chaotic pendulum 67
The need for models of nonlinear oscillations 67
The case of a nonlinear forced pendulum with friction (Model 4) 68
11 Linear models in social processes: the case of two interacting
populations 71
Introduction 71
The linear model of two interacting populations 72
Some qualitative aspects of linear model dynamics 73
The solutions of the linear model 76
Complex conjugate roots of the characteristic equation: the
values of the two populations fluctuate 84
12 Nonlinear models in social processes: the model of
Volterra Lotka and some of its variants in ecology 93
Introduction 93
The basic model 94
A non punctiform attractor: the limit cycle 98
Carrying capacity 101
Functional response and numerical response of the predator 103
13 Nonlinear models in social processes: the Volterra Lotka
model applied to urban and regional science 108
Introduction 108
Model of joint population income dynamics 108
The population income model applied to US cities and to Madrid 113
The symmetrical competition model and the formation of niches 118
PART 2 From Nonlinearity to Chaos 123
14 Introduction 125
15 Dynamical systems and chaos 127
Some theoretical aspects 127
Two examples: calculating linear and chaotic dynamics 131
Contents
The deterministic vision and real chaotic systems 135
The question of the stability of the solar system 137
16 Strange and chaotic attractors 141
Some preliminary concepts 141
Two examples: Lorenz and Rossler attractors 146
A two dimensional chaotic map: the baker's map 150
17 Chaos in real systems and in mathematical models 154
18 Stability in dynamical systems 159
The concept of stability 159
A basic case: the stability of a linear dynamical system 161
Poincare and Lyapunov stability criteria 163
Application of Lyapunov's criterion to Malthus' exponential
law of growth 168
Quantifying a system's instability: the Lyapunov exponents 171
Exponential growth of the perturbations and the predictability
horizon of a model 176
19 The problem of measuring chaos in real systems 179
Chaotic dynamics and stochastic dynamics 179
A method to obtain the dimension of attractors 183
An observation on determinism in economics 186
20 Logistic growth as a population development model 190
Introduction: modelling the growth of a population 190
Growth in the presence of limited resources: Verhulst equation 191
The logistic function 194
21 A nonlinear discrete model: the logistic map 199
Introduction 199
The iteration method and the fixed points of a function 201
The dynamics of the logistic map 204
22 The logistic map: some results of numerical simulations
and an application 214
The Feigenbaum tree 214
An example of the application of the logistic map to
spatial interaction models 224
23 Chaos in systems: the main concepts 231
Contents
PART 3 Complexity 237
24 Introduction 239
25 Inadequacy of reductionism 240
Models as portrayals of reality 240
Reductionism and linearity 241
A reflection on the role of mathematics in models 243
A reflection on mathematics as a tool for modelling 246
The search for regularities in social science phenomena 249
26 Some aspects of the classical vision of science 253
Determinism 253
The principle of sufficient reason 257
The classical vision in social sciences 259
Characteristics of systems described by classical science 261
27 From determinism to complexity: self organization, a new
understanding of system dynamics 266
Introduction 266
The new conceptions of complexity 268
Self organization 271
28 What is complexity? 275
Adaptive complex systems 275
Basic aspects of complexity 277
An observation on complexity in social systems 280
Some attempts at defining a complex system 281
The complexity of a system and the observer 285
The complexity of a system and the relations between its parts 286
29 Complexity and evolution 291
Introduction 291
The three ways in which complexity grows according
to Brian Arthur 291
The Tierra evolutionistic model 295
The appearance of life according to Kauffman 297
30 Complexity in economic processes 301
Complex economic systems 301
Synergetics 304
Two examples of complex models in economics 307
A model of the complex phenomenology of the financial markets 309
Contents
31 Some thoughts on the meaning of'doing mathematics' 315
The problem of formalizing complexity 315
Mathematics as a useful tool to highlight and express
recurrences 320
A reflection on the efficacy of mathematics as a tool to
describe the world 323
32 Digression into the main interpretations of the foundations
of mathematics 329
Introduction 329
Platonism 330
Formalism and 'les Bourbaki' 331
Constructivism 336
Experimental mathematics 340
The paradigm of the cosmic computer in the vision of
experimental mathematics 341
A comparison between Platonism, formalism, and constructivism
in mathematics 343
33 The need for a mathematics of (or for) complexity 348
The problem of formulating mathematical laws for complexity 348
The description of complexity linked to a better
understanding of the concept of mathematical infinity:
some reflections 351
References 356
Subject index 375
Name index 380 |
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| id | DE-604.BV021284824 |
| illustrated | Illustrated |
| index_date | 2024-07-02T13:48:10Z |
| indexdate | 2024-07-09T20:34:42Z |
| institution | BVB |
| isbn | 0198567901 019856791X 9780198567912 |
| language | English Italian |
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| spelling | Bertuglia, Cristoforo S. Verfasser aut Nonlinearità, caos, complessità Nonlinearity, chaos, and complexity the dynamics of natural and social systems Cristoforo Sergio Bertuglia ; Franco Vaio 1. publ. Oxford [u.a.] Oxford Univ. Press 2005 XV, 387 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Includes bibliographical references and indexes. - Formerly CIP Aus dem Ital. übers. Chaostheorie Chaostheorie (DE-588)4009754-7 gnd rswk-swf Nichtlineare Dynamik (DE-588)4126141-0 gnd rswk-swf Nichtlineare Dynamik (DE-588)4126141-0 s DE-604 Chaostheorie (DE-588)4009754-7 s Vaio, Franco Verfasser aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014605773&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Bertuglia, Cristoforo S. Vaio, Franco Nonlinearity, chaos, and complexity the dynamics of natural and social systems Chaostheorie Chaostheorie (DE-588)4009754-7 gnd Nichtlineare Dynamik (DE-588)4126141-0 gnd |
| subject_GND | (DE-588)4009754-7 (DE-588)4126141-0 |
| title | Nonlinearity, chaos, and complexity the dynamics of natural and social systems |
| title_alt | Nonlinearità, caos, complessità |
| title_auth | Nonlinearity, chaos, and complexity the dynamics of natural and social systems |
| title_exact_search | Nonlinearity, chaos, and complexity the dynamics of natural and social systems |
| title_exact_search_txtP | Nonlinearity, chaos, and complexity the dynamics of natural and social systems |
| title_full | Nonlinearity, chaos, and complexity the dynamics of natural and social systems Cristoforo Sergio Bertuglia ; Franco Vaio |
| title_fullStr | Nonlinearity, chaos, and complexity the dynamics of natural and social systems Cristoforo Sergio Bertuglia ; Franco Vaio |
| title_full_unstemmed | Nonlinearity, chaos, and complexity the dynamics of natural and social systems Cristoforo Sergio Bertuglia ; Franco Vaio |
| title_short | Nonlinearity, chaos, and complexity |
| title_sort | nonlinearity chaos and complexity the dynamics of natural and social systems |
| title_sub | the dynamics of natural and social systems |
| topic | Chaostheorie Chaostheorie (DE-588)4009754-7 gnd Nichtlineare Dynamik (DE-588)4126141-0 gnd |
| topic_facet | Chaostheorie Nichtlineare Dynamik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014605773&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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