Smart Modeling and Simulation for Complex Systems: Practice and Theory

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Meanwhile, smart systems such as multi-agent systems have demonstrated advantages and great potentials in modelling and simulating complex systems. Each paper was peer reviewed by three PC members. We solicited papers on all aspects of smart simulation and modelling of complex systems through using agent and other AI technologies.

They are, for instance, being studied in the network modelling, microsimulation and modelling, social influence modelling, disaster modelling, environment modelling, power market modelling, and idea discovery process modelling. Finally, we would like to extend our sincere thanks to all authors. Emerging properties, characterising relationships between the micro level and the macro level of the system, contribute to ensure this global regulation.

A full variety of networks connecting cities interfere in different time and spatial scales. Moreover, geographic space is in constant evolution, especially since the industrial revolution. The increasing speed of communication has tremendously changed the relative positions of cities and towns. This is mentioned for instance by Korcelli or Klaassen Bretagnolle and alii, The boundaries of the familiar territory, frequently visited by the residents of the centre, are moving forward according to the innovations in transport technology.

The destiny of the places which are integrated in these waves of dilatation can then be completely reversed in a few decades. The example of Saint-Denis Figure 5 , located in the north of Paris, illustrates these transformations. During Middle Age, Saint-Denis was a real city, separated from Paris by a distance of two hours walking about 7 km.

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It was a stop on the Roman road which led to Rouen, then receiving important royal privileges abbey and fair. With the transport revolution, at the beginning of the nineteenth century, Saint-Denis felt under the isochronic line of one hour distance from Paris, and was propelled to the role of an industrial suburb metallurgy, chemical industry and stocking activities.

The population was multiplied by a factor 15 within less than a century. With the revolution in communication and the fast railway lines of the second half of the twentieth century, the status of Saint-Denis is changing again, because it now belongs to the Parisian hyper-centre, which is delimited roughly by the isochronic line of half an hour an argument which is often presented by urban developers or actors who want to attract new firms and residents.

Registered offices and high technology activities multimedia, information processing settle in this locality and the former industrial activities and workers are moving away to farther suburbs. During the Middle Age, these three cities were important nodes, at the national scale and even at the international level. From the eighteenth and the beginning of the nineteenth century, various technical improvements concerning roads and coaches have almost divided travel times by two.

The three cities remained however important nodes at the national and regional levels. With the railway transports, they felt under the isochronic line of one day from Paris. While entering the influence field of the Parisian region, they underwent a relative decline at the national and international scale. During the second half of twentieth century, they were not served by an airport except a regional one , fast train TGV or highway crossing Bretagnolle, From their situation, now at less than two hours from Paris, it can be expected that they will become soon integrated in the dilatation wave of the Parisian urban field the process will be accelerated through the building of the East TGV line, including a stop at Reims: the share of commuters toward Paris has already begun to increase.

The first models were mainly conceived as systems of non linear differential equations describing the evolution of state variables at a macro-level, the lower level interactions being summarised in relations or in parameters. As interactions are non linear, the systems are not attracted towards a pre-determined equilibrium in physics they would be said non ergodic , a shock linked with the amplification of some internal fluctuation, or with an external perturbation, that is, a small change in the parameters of the model, can modify the dynamic trajectory of the systems and persist as a determinant of their further qualitative structure, according to a bifurcation.

For instance, a small change in preference of consumers for large size and diversity of shops, as well as a variation in the price of oil, can produce a spatial concentration of trade in a major centre or its dispersion in a multitude of small centres Wilson, , Allen et al. Weidlich and G. On the contrary, models of micro-simulation integrated a lot of details about the behaviour and familial or professional career of individuals, but did not pay so much attention to the evolution of the resulting structures at the macro level Holm, Sanders, Compared to these earlier representations of self-organisation in models, the actual notion of emergent properties refers to a more explicit modelling of individual behaviour and interactions, usually in agent based models or in multi-agent systems.

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Emergent properties appear at a higher level of aggregation than the original description of the system. We analyse here one example connecting the meso and macro levels of observations. They are produced by the multiple interactions which occur between individual towns and cities. Indeed, these interactions between individual towns and cities, when observed at very short time intervals, seem like local fluctuations, which bring about stochastic variations of city sizes. These variations are independent from the initial sizes of the cities 2.

If we use the census data for the French cities, the length of the intervals is between five and ten years, from to We actually observe growth rates which are fluctuating around the average, even in the case of largest cities, which are nevertheless continuously growing during these two centuries when characterised by a cluster analysis Pumain, Saint-Julien, But the evolution of their relative weight within the urban system is quite different, with oscillations around zero which mean short term fluctuations of the relative attractivity of each metropolis within the urban system.

We have plotted for the largest French cities Figure 6 its relative weight at one census date on X-axis and at the following census date on Y-axis.

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On the contrary, we observe spiral patterns, which characterise cyclic variations of growth, sometimes positive, sometimes negative. The cycles are not synchronous, but exhibit more or less regular patterns. Paris, Lyon and Marseilles, for instance, seem to follow a very regular cycle increasing then decreasing their relative weight , whereas Lille, Toulouse or Nantes have more complicated stories.

The urban system is self-regulating, by the way of the multiple interactions which allow successive adjustments and progressive adaptations to the external perturbations or to the endogenous innovations. This dynamic stability can be perceived, for instance, when plotting rank-size distribution over several centuries Figure 7. The different curves are very similar, rendering invisible the multiple local variations in the individual rankings between census dates, which were yet well established by F.

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Pumain The similarity of the curves can also be characterised by measuring the slopes of the adjusted Zipf rank-size distributions, which are interpreted as indices of concentration. The values are growing up very slightly and very continuously, from the eighteenth century to nowadays 3 Bretagnolle and alii, The discovery of the New World in and the invention of the steam engine, in , gave twice a decisive advantage to the Atlantic cities, compared to Mediterranean ones, but these tremendous changes did not generate a sudden bifurcation of the whole system. On the contrary, we observe a very slow modification of the spatial pattern of the most prominent cities as defined by the population potential model from the south to the north, with a bi-polar structure which maintains the equilibrium of the system from the 14th to the 17th century, transferring the centre of the world economy of the time from northern Italy to the Belgian, Dutch and then English metropolises Braudel, , de Vries, , Bretagnolle and alii, In this model, the environment is represented by cells having different kinds of resources, for agricultural production or industrial purposes exploited only from year on , and various facilities or obstacles for circulation.

They can be allocated randomly or according to a specific pattern. Towns are emerging as centres of accumulation of population and wealth, through first the trading of agricultural surplus in their surrounding cells, then from their competition for the acquisition of other urban functions, as other types of trades, or administrative roles. Interurban competition is simulated by relating profits from trade or taxes and growth rates, with a random factor. Meanwhile, the spatial range of interactions is increased when cities acquire new functions and with technological progress going.

As a result, different patterns of towns and cities in terms of spatial and hierarchical distribution are emerging. It is conceived for a larger number of agents several thousands. It also includes a better representation of the competitive interaction between cities, through the introduction of two new agents which make explicit the role of the functions of innovation and governance within the dynamics of the urban system. This is a way to complete the theory of urban systems within the framework of complex systems theory, by substantiating the growth process in social terms.

What make cities growth? Since Schumpeter, innovations, especially entrepreneurial ones, are theorised as making the economic basis for further urban growth. A recent review of the literature on industrial districts, innovation and learning processes in regional and urban systems McKinnon et al. This evolution involves systematic, time-oriented changes in major circumstances of the system over time, including the demographic and urban transitions, the increase in gross and per capita economic wealth, the trendy increase in the speed of transportation means, as well as the recurrent appearance of technical, economic and cultural innovation.

Thus, it is this social, historical evolution which supports the dynamics of urban systems, even if in a concrete way it is made through the mechanism of interurban interactions. Actually, we do not know yet how to make these large evolutionary trends to emerge, and they are represented in an exogenous way within the model, whereas it is possible to represent the endogenous process of building an urban hierarchy from the interactions between cities. A city participates to this interurban competition through the functions or economic specialisation that it successively acquires over time.

A function enable a city to supply a type of product or service to other cities, which provide more or less returns in terms of economic growth and attractivity on population, according to the level of productivity of that function. The criteria for establishing a list of relevant specialisation for the definition of urban functions are related to an evolutionary perspective, under the main hypothesis that a narrow connexion exist between the relative dynamics of an urban entity in the system of cities and the innovation cycles that the city has adopted or to which it has better adapted.

The question is to identify, for the entire system of cities, which innovation cycles have produced noticeable urban specialisation, affecting in a durable way the relative evolution of the specialised cities, and for each city, which are the specialisation that correspond at best to its actual and potential trajectory.


A limited number of urban functions were selected as representative of the major economic cycles which gave rise to differential urban growth and cities specialisation over the past four centuries Figure 8. Cities as agents have a total or partial as constrained by the network of their partner cities information about the emergence of new functions which remains exogenous to the model.

Cities also have a power of decision to invest in that innovation, according to the wealth they have previously accumulated and to their line of urban strategy, that can be more or less risk-oriented.

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For example, the urban functions are essential attributes of the cities. They do not give an exhaustive representation of the economic profiles of the cities, since they are attributed only to the cities having developed a major specialisation in a particular sector of activity during the corresponding innovation cycle. Long distance trade, maritime transport, part of tourism activities, or manufacturing industry, are following this type of spatial interaction rule Figure 8.

While such ideas appear challenging for geography, we want to draw attention on what could be a more specific contribution of our discipline to this developing field of research. But if we want to learn something about the real world from such exercises, by confronting the results of simulation with observation, there are two essential points: first is that these models should refer to the existing knowledge when defining the agents relevant attributes and behaviour, for instance from surveys in demography, social or economic, instead of inventing intuitive and untested rules; and simulated results should be not just presented but evaluated by using statistics or spatial analysis as benchmarks for testing the plausibility of the simulated emergent structures.

We should then keep in mind that models are useful if they can reasonably be integrated in the existing knowledge, formalising it and possibly producing new results. Table 1: Population of Italian agglomerations larger than unhabitants in , according to three data bases populations in thousands. Allen P. Amsterdam, Gordon and Breach. Allen, P. Journal of Social and Biological Structures 2, Geographical Analysis 11, Environment and Planning 13, Anderson C.

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