Nonlinearity, Chaos, and Complexity: The Dynamics of Natural and Social Systems Book

1	Introduction	3
2	Modelling	10
3	The origins of system dynamics : mechanics	19
4	Linearity in models	27
5	One of the most basic natural systems : the pendulum	32
6	Linearity as a first, often insufficient approximation	39
7	The nonlinearity of natural processes : the case of the pendulum	46
8	Dynamical systems and the phase space	49
9	Extension of the concepts and models used in physics to economics	60
10	The chaotic pendulum	67
11	Linear models in social processes : the case of two interacting populations	71
12	Nonlinear models in social processes : the model of Volterra-Lotka and some of its variants in ecology	93
13	Nonlinear models in social processes : the Volterra-Lotka model applied to urban and regional science	108
14	Introduction	125
15	Dynamical systems and chaos	127
16	Strange and chaotic attractors	141
17	Chaos in real systems and in mathematical models	154
18	Stability in dynamical systems	159
19	The problem of measuring chaos in real systems	179
20	Logistic growth as a population development model	190
21	A nonlinear discrete model : the logistic map	199
22	The logistic map : some results of numerical simulations and an application	214
23	Chaos in systems : the main concepts	231
24	Introduction	239
25	Inadequacy of reductionism	240
26	Some aspects of the classical vision of science	253
27	From determinism to complexity : self-organization, a new understanding of system dynamics	266
28	What is complexity?	275
29	Complexity and evolution	291
30	Complexity in economic processes	301
31	Some thoughts on the meaning of 'doing mathematics'	315
32	Digression into the main interpretations of the foundations of mathematics	329
33	The need for a mathematics of (or for) complexity	348