Advances in Complex Systems

Complex systems may often be characterized by their hierarchical dynamics. In this paper we present a method and an operational algorithm that automatically infer this property in a broad range of systems — discrete stochastic processes. The main idea is to systematically explore the set of projections from the state space of a process to smaller state spaces, and to determine which of the projections impose Markovian dynamics on the coarser level. These projections, which we call Markov projections, then constitute the hierarchical dynamics of the system. The algorithm operates on time series or other statistics, so a priori knowledge of the intrinsic workings of a system is not required in order to determine its hierarchical dynamics. We illustrate the method by applying it to two simple processes — a finite state automaton and an iterated map.

We use a notion of causal independence based on intervention, which is a fundamental concept of the theory of causal networks, to define a measure for the strength of a causal effect. We call this measure "information flow" and compare it with known information flow measures such as transfer entropy.

This paper generalizes previous results concerning the definitions of physical temperature and pressure in nonextensive statistical thermodynamics. The novelty is that both the internal energy and the volume are no longer additive functions. The new approach is referred to as "fully" nonextensive thermodynamics. The physical temperature is different from the inverse of the Lagrange multiplier. This fact changes the form of some usual thermodynamic relations. For example, the Clausius definition of the thermodynamic entropy has to be modified. As an application, the classical gas model is examined with statistical calculations performed under the Tsallis–Mendes–Plastino formalism of nonextensive thermodynamics. The specific heat expression differs from the one encountered in ordinary extensive thermodynamics but the equation of state keeps the same form.

We analyze the phase response of a system shaped as a ring of overdamped bistable and noisy oscillators coupled directionally. This device, which operates in the regime of stochastic resonance, may act as a short-term memory device. In the present work we show that in this regime the system presents partial phase synchronization with an average frequency equal to the external one. For lower/greater values of noise the system becomes more/less ordered, which is characterized by a statistical measure.

In this paper, we consider a predator–prey chemostat model with ratio-dependent Monod type functional response and periodic input and washout at different fixed times. We obtain an exact periodic solution with substrate and prey. The stability analysis for this periodic solutions yields an invasion threshold for the period of pulses of the predator. When the impulsive period is more than the threshold, there are periodic oscillations in the substrate, prey, and predator. If the impulsive period further increases, the system undergoes a complex dynamic process. By analyzing bifurcation diagrams, we can see that the impulsive system shows two kinds of bifurcation, which are period-doubling and period-halving.

We study an impulsive delay differential predator–prey model with Holling type II functional response. The stability of the trivial equilibrium is analyzed by means of impulsive Floquet theory providing a sufficient condition for extinction. Using coincidence degree theory we show the existence of positive periodic solutions. The system is then analyzed numerically, revealing that the presence of delays and impulses may lead to chaotic solutions, quasi-periodic solutions, or multiple periodic solutions. Several simulations and examples are presented.

Endogenous, ideas-led growth theory and the literature on agent-based modeling with neighborhood effects are crossed. In an economic overlapping generations framework, it is shown how social interactions and neighborhood effects are of vital importance in the endogenous determination of the long run number of skilled workers and therefore of the growth prospects of an economy. Neighborhood effects interact with the initial distribution of skilled agents across space and play a key role in the long run stabilization of the number of skilled individuals. Our model implies a tendency toward segregation, with a possibly positive influence on growth, if team effects operate. The long run growth rate is also shown to depend on the rate of time preference. Initial circumstances are of vital importance for long run outcomes. A poor initial education endowment will imply a long run reduced number of skilled workers and a mediocre growth rate, so there is no economic convergence tendency. On the contrary, poor societies will grow less, or will even fall into a poverty trap, and will diverge continuously from richer ones.

Our analysis, conducted using the GDP and the GDP deflator time series (OECD source; 1960–2001) for the G7 countries, shows the robustness of the negative covariance between the GDP and its deflator, but only over long run horizons. Through wavelet decomposition we evaluate the price–output relationship at different time scales, where most countries reveal similar patterns. More precisely, at short time scales a positive correlation seems to appear whereas, and consequently, a regime switch occurs at a time horizon of about two years leading to a negative relationship for higher horizons. These results seem to suggest that the negative or acyclical relationship usually found after the 1960s may be the composite effect of different time scale correlations, where the four-year-horizon component seems to have the greatest influence. In particular for Canada, France, and Italy we observe something like a rotation of the price–output relationship between the countercyclical and the procyclical relationship. Finally, our analysis shows that even the relationship between the two series does not seem to be very stable regarding the lead and lag structure also. The phase is nonlinear for all the countries and, consequently, the group delay (the lag) is not constant. In particular, looking at the time scale we observe an inversion of the local monotonicity at the frequency of about 0.3–0.35 for all G7 countries.

The practice of detecting power laws and scaling behaviors in economics and finance has gained momentum in the last few years, due to the increased use of concepts and methods first developed in statistical physics. Some disappointment has emerged in the economic profession, however, as regards the models proposed so far to theoretically explain these phenomena. In this paper we aim to address this criticism, showing that scaling behaviors can naturally emerge in a multiagent system with optimizing interacting units characterized by financial fragility.

Industrial networks offer a prime example of the tension between system stability and change. Change is necessary as a response to environmental variation, whereas stability provides the underpinning for long-term investment and the exploitation of efficiencies. Whilst one of the key themes in industrial network research has been the dynamics of change, relatively little work, empirical or theoretical, has been devoted to the dynamics of stability. This paper presents a new approach to this problem by using Boolean networks, which were originally devised by Stuart Kauffman as an abstract model of genetic networks. The elements in the model are connected by rules of Boolean logic, and a novel aspect of this research is that the elements represent the industrial network exchanges rather than stock entities (the organizations). The model structure consists of interactions between the exchanges, and the results represent the pattern of exchange episodes. A total of 42 networks were modeled and the dynamics analyzed in detail, and five of these cases are presented in this paper. The models produced realistic behavior and provided some insights into the reasons for stability in industrial networks.

No influence was seen when in two models with memory effects the populations were drastically decreased after equilibrium was established, and then allowed to increase again.