Advances in Complex Systems

The modelling of financial markets presents a problem which is both theoretically challenging and practically important. The theoretical aspects concern the issue of market efficiency which may even have political implications (Cuthbertson, 1996), whilst the practical side of the problem has clear relevance to portfolio management (Elton and Gruber, 1995) and derivative pricing (Hull, 1997). Up till now all market models contain "smart money" traders and "noise" traders whose joint activity constitutes the market (De Long et al., 1990; Bak et al., 1997). On a short time scale this traditional separation does not seem to be realistic, and is hardly acceptable since all high-frequency market participants are professional traders and cannot be separated into "smart" and "noise". In this paper we present a "microscopic" model with homogenuous quasi-rational behaviour of traders, aiming to describe short time market behaviour. To construct the model we use an analogy between "screening" in quantum electrodynamics and an equilibration process in a market with temporal mispricing (Ilinski, 1997; Dunbar, 1998). As a result, we obtain the time-dependent distribution function of the returns which is in quantitative agreement with real market data and obeys the anomalous scaling relations recently reported for both high-frequency exchange rates (Ghashghaie et al., 1996, S&P500 (Mantegna and Stanley, 1994) and other stock market indices (Bouchaud and Sornette, 1994; Matacz, 1997).

Ant Colony Optimization (ACO) is a promising new approach to combinatorial optimization. Here ACO is applied to the traveling salesman problem (TSP). Using a genetic algorithm (GA) to find the best set of parameters, we demonstrate the good performance of ACO in finding good solutions to the TSP.

The paper examines the appearance of on-off intermittency and riddled basins of attraction in a system of two coupled one-dimensional maps, each displaying type-III intermittency. The bifurcation curves for the transverse destablilization of low periodic orbits embeded in the synchronized chaotic state are obtained. Different types of riddling bifurcation are discussed, and we show how the existence of an absorbing area inside the basin of attraction can account for the distinction between local and global riddling as well as for the distinction between hysteric and non-hysteric blowout. We also discuss the role of the so-called mixed absorbing area that exists immediately after a soft riddling bifurcation. Finally, we study the on-off intermittency that is observed after a non-hysteric blowout bifurcaton.

The paper applies continuation methods to examine fundFigureamental features of the complex dynamics that can arise in a cascaded system of population dynamic models. The individual model describes a bacterial population interacting with a population of viruses that attack the cells and exploit their reproductive system for their own replication. Coupling between the subsystems is brought about through a unidirectional flow of primary resources. In this way the individual subsystem is modulated by the varying nutrient concentration in the overflow from the upstream habitat.

Synchronization of a single subsystem to an external periodic forcing exhibits an unusual bifurcation structure with global bifurcations appearing already at the lowest forcing amplitudes. This peculiarity is also observed for autonomous systems of two and three coupled habitats. Finally, local and global synchronization phenomena are investigated for a chain of 20 coupled population pools.

Rainforests are legendary because their extreme species richness. In the richest rain forests every second tree on a hectare is a differnt species. As a consequence, most species are rare. Using field data from studies in dfiferent parts of the world, we show that species-rich plots often display a distribution of number of species N_s(I) represented by I individuals with a power-law shape N_s(I)∝I^-β with β≈1.5. Power laws are characteristic (but not exclusive) of systems poised close to critical points and this is supported by the analysis of the gap distribution over space in the Barro Colorado Island forest, which has been shown to be fractal. Here we propose a new model of rainforest dynamics which is able to account for a wide set of observations, strongly suggesting that indeed rainforests would be organized close to instability points, showing strongly path-dependent dynamics.

The conditions under which the aggregation of information from interacting agents results in a stable or an unstable collective outcome is an important puzzle in the study of complex systems. We show that if a complex system of aggregated choice respects a mutual knowledge structure, then the prospects of a stable collective outcome are considerably improved. Our domain-independent results apply to collective choice ranging from perception, where an interpretation of sense data is made by a collection of perceptual modules, to social choice, where a group decision is made from a set of preferences held by individuals.

This paper presents an unified overview of a new family of distributed algortithms for routing and load balancing in dynamic communication networks. These new algorithms are described as an extension to the classical routing algorithms: they combine the ideas of online asynchronous distance vector routing with adaptive link state routing. Estimates of the current traffic condition and link costs are measured by sending routing agents in the network that mix with the regular information packets and keep track of the costs (e.g. delay) encountered during their journey. The routing tables are then regularly updated based on that information without any central control nor complete knowledge of the network topology. Two new algorithms are proposed here. The first one is based on round trip routing agents that update the routing tables by backtracking their way after having reached the destination. The second one relies on forward agents that update the routing tables directly as they move toward their destination. An efficient co-operative scheme is proposed to deal with asymmetric connections. All these methods are compared on a simulated network with various traffic loads; the robustness of the new algorithms to network changes is proved on various dynamic scenarii.

Recent studies on the fossil record time series has suggested that there is consistent evidence for self-similarity i.e. long-range correlations with power-law behavior. The existence of such fractal strucutes means that, when looking at a given time frame, some basic properties remain the same if a change of scale is performed. In other words, there is no characteristic time scale, as we could expect if some type of periodic or other low-dimensional dynamics were present. A possible explanation for such long-range order is a dynamical process operating at all scales, as it is the case for systems in the neighborhood of critical points. In this paper these results are further explored by extending previous data analysis and examining the relevance of recent theoretical approaches to the statistical features of the fossil record. The presence of long-range correlations is shown through Hurst analysis using non-interpolated data series from the Fossil Record 2 database. As shown in previous studies, such correlations span over hundreds of millions of years and are compared with a simple model of large-scale evolution displaying self-organized criticality.

Honey bee nectar foragers returning to the hive experience a delay as they search for a receiver bee to whom they transfer their material. In this paper I describe the simulation of the "threshold rule" (Seeley, 1995) which relates the magnitude of this search delay to the probability of performing a recriutment dance — waggle dance, tremble dance, or no dance. Results show that this rule leads to self-organised near-optimal worker allocation in a fluctuating environment, is extremely robust, and operates over a wide range of parameter values. The reason for the robustness appears to be the particular sytem of feedbacks that operate within the system.