Günter Haag

How to control a chaotic economy

An economic system which exhibits chaotic behaviour has been stabilized on various periodic orbits by use of the Ott-Grebogi-Yorke method. This procedure has been recently applied to controlling chaotic phenomena in physical, chemical and biological systems. We adopt this method successfully for Feichtingers generic model of two competing firms with asymmetrical investment strategies. We show that the application of this control method to the particular economic process considered brings a substantial advantage: one can easily switch from a chaotic trajectory to a regular periodic orbit and simultaneously improve the systems economic properties. Numerical simulations are presented in order to illustrate the effectiveness of the whole procedure.

The rank-size distribution of settlements as a dynamic multifractal phenomenon

Abstract The rank-size distribution in a system of settlements is considered as a multifractal phenomenon. The occurence and temporal stability of the rank-size distribution is obtained as the result of a dynamic self-organization process in the nested system of settlements. The inherent time scale of this self-organization process and the obtained hierarchical structure are related to low intersettlement mobility of urban population, a tendency of the population to agglomerate, as well as distance and preference effects. A well-known migration model is used with three different approaches for the attractivity of a settlement for comparative purposes.

Destructive role of competition and noise for control of microeconomical chaos

Abstract The problem of control of chaos in a microeconomical model describing two competing firms with asymmetrical investment strategies is studied. Cases when both firms try to perform the control simultaneously or when noise is present are considered. For the first case the resulting control efficiency depends on the system parameters and on the maximal values of perturbations of investment parameters for each firm. Analytic calculations and numerical simulations show that competition in the control leads to ‘parasitic’ oscillations around the periodic orbit that can destroy the expected stabilization effect. The form of these oscillations is dependent on non-linear terms describing the motion around periodic orbits. An analytic condition for stable behaviour of the oscillation (i.e. the condition for control stability) is found. The values of the mean period of these oscillations is a decreasing function of the amplitude of investment perturbation of the less effective firm. On the other hand, amplitudes of market oscillations are increasing functions of this parameter. In the presence of noise the control can be also successful provided the amplitude of allowed investment changes is larger than some critical threshold which is proportional to the maximal possible noise value. In the case of an unbounded noise, the time of laminar epochs is always finite but their mean length increases with the amplitude of investment changes. Computer simulations are in very good agreement with analytical results obtained for this model.

A Non-Linear Dynamic Model for the Migration of Human Populations

The purpose of this paper is to present a model of migration and birth-death processes for interacting populations. This model is a typical application of the general concepts set out in the book Concepts and Models of a Quantitative Sociology (Weidlich and Haag, 1982), while a similar type of model has been reported on elsewhere (Weidlich and Haag, 1980a). There exists an extensive literature on birth-death and migration processes of biological species, of which the books of May (1973), Rosen (1970), Pielou (1969), and Haken (1977) are only a small selection. This literature includes stochastic models as well as mean value models.

An Integrated Model of Transport and Urban Evolution

Prefaces.- Part I: 1. Introduction 2. China in a State of Flux 3. Nanjing City and Greater Nanjing 4. Traffic Development in China (Especially Within the Region of Nanjing).- Part II: 5. The Integrated Transport and Evolution Model 6. The Data Situation of Nanjing 7. Adaptation of ITEM to the Specific Data Situation of Nanjing.- Part III: 8. Methodology (Analysis and Forecasting) of the Traffic and Urban/Regional Situation of Nanjing City 9. Analysis of the Transport System and of the Population Development 10. Forecasting of the Traffic and Urban/Regional Development of Nanjing City for Different Scenarios 11. Summary and Recommendations.- Acknowledgement.- Appendices.- References

Active Stabilization of a Chaotic Urban System

A new method to stabilize dynamical systems by forcing the system variables into the desired unstable stationary point is proposed. The key conception of the method is based on parametric perturbation. This means that the equations of motion are influenced by continuous variation of some selected parameters. Thus – without using any external forces – the motion of the system approaches the chosen unstable stationary point. The variation of the parameters will vanish after the successful stabilization. Therefore, the system and its parameters are changed during the control process only. The algorithm is applied to an urban system within a metropolitan area obeying a Lorenz-type dynamics as well as to the Henon attractor as an example for a discrete scenario.

Outline of a Formal Theory of Long-Term Economic Cycles

As unemployment persists in many regions and industries in the developed world, the Kondratieff-wave model has returned into favor with those who wish to say why unemployment crept in and persists. The trouble is that the gradualism built into the long-wave concept overshadows the true causality: The underlying change in industry structure, and the swiftness of possible reversal to full employment if investors are not discouraged by wrong notions of gradualism. The main objective, thus, of this chapter is to bring back hope. There exist faster ways to full employment than suggested by the wave model.

A new theory of nested decision processes with memory. Part I: The stochastic framework

Choice problems are concerned with agents (such as individuals and firms) who have to select one alternative from a set of alternatives. Static models for such processes are well known, e.g., the multinomial logit model. However, such models are limited in their usefulness since the time factor is excluded. In addition, the introduction of social interaction among the individuals involved in the choice process is not allowed in most models. This paper aims to overcome these limitations. The choice process is treated in a stochastic framework, using a master equation approach. This means that uncertainties can be introduced in the perception of the relative advantages of the choice alternatives as seen by the agent. It is well known that synergy effects play a crucial role in most choice considerations. Those effects can be treated via the introduction of appropriate transition rates and yield the dynamics of the probability that a certain distribution of choices can be found, with the multinomial logit solution as a limiting case. Nested decision structures, i.e., decisions at a certain time that are influenced by all previous choices are of greater interest. The dynamic modeling of such a sequence of decisions requires new ideas and a detailed analysis of every single step. The possibility of both the arisal of new alternatives and of the disappearance of old ones must be taken into account. Small differences in subsequent utilities could lead to a dynamic selection process of a specific alternative. The stochastic choice model can be applied to problems of neural networks, to innovation theory and travel choice, among others.

Comparative analysis of interregional migration.

The interregional migration processes within the six countries (FRG, Canada, France, Israel, Italy, Sweden), which have been described in detail in Part II, Chapters 4 to 9, are now studied under comparative aspects in this chapter.

Employment and Education as Non-Linear Network-Populations, Part I: Theory, Categorization and Methodology

It would, perhaps, be premature to speculate here upon the question whether the methods of abstract science are likely at any future day to render service in the investigation of social problems at all commensurate with those which they have rendered in various departments of physical inquiry. An attempt to resolve this question upon pure a priori grounds of reasoning would be very likely to mislead us...We learn that we are not to expect, under the dominion of necessity, an order perceptible to human observation, unless the play of its producing causes is sufficiently simple; nor, on the other hand, to deem that free agency in the individual is inconsistent with regularity in the motions of the system of which he forms a component unit.