Advances in Complex Systems

Stochastically forced business cycle model is considered. We study a phenomenon of the noise-induced generation of complex mixed-mode oscillations in zones where the deterministic model exhibits a single attractor (equilibrium or limit cycle). A probabilistic mechanism of the transition from unimodal oscillations to the intermittency of small- and large-amplitude stochastic oscillations is investigated on the base of the stochastic sensitivity functions technique. We show that such intermittency, connected with the nonuniformity of phase portrait, can be parametrically analyzed by the confidence domains method.

In this paper, we use the financial network contagion model of Gai P. and Kapadia S. [Contagion in financial networks, Proc. R. Soc. A 466 (2010) 2401–2423] to investigatethe interaction of several types of heterogeneity found in real world banking systems. The first source of heterogeneity originates in the distribution of assets across banks in the financial system. The second source is in how individual banks then distribute these assets among their neighbors. We characterize how these two sources of heterogeneity interact to affect the probability and extent of financial contagions in three network structures. We find that greater heterogeneity has a stabilizing effect for networks that are sparsely connected and a destabilizing effect for networks that are highly interconnected. Finally, we consider multiple sequential shocks and find that when banks redistribute assets following an initial mild contagion it increases the stability, on average, of the system to subsequent shocks originating at weakened banks.

Because the dynamics of complex systems is the result of both decisive local events and reinforced global effects, the prediction of such systems could not do without a genuine multilevel approach. This paper proposes to found such an approach on information theory. Starting from a complete microscopic description of the system dynamics, we are looking for observables of the current state that allows to efficiently predict future observables. Using the framework of the information bottleneck (IB) method, we relate optimality to two aspects: the complexity and the predictive capacity of the retained measurement. Then, with a focus on agent-based models (ABMs), we analyze the solution space of the resulting optimization problem in a generic fashion. We show that, when dealing with a class of feasible measurements that are consistent with the agent structure, this solution space has interesting algebraic properties that can be exploited to efficiently solve the problem. We then present results of this general framework for the voter model (VM) with several topologies and show that, especially when predicting the state of some sub-part of the system, multilevel measurements turn out to be the optimal predictors.

Certain capacity degradation levels increase travel times on road networks, while traffic demand remains met. Resilience of a road network is higher, if it can take-in higher levels of degradation without leaving any part of the demand unmet. It is important for planners to quantify this, and it can be obtained as the output of an optimization problem. The resultant measure of resilience is demand-specific. To generalize the resilience measure, its sensitivity to change in demand should be studied. We observe that irrespective of the difference in network size or network topology, resilience decreases with increase in demand. We perform computational experiments on different network topologies to investigate the relationship between network resilience and traffic demand. Based on this, we introduce the area under the demand-resilience curve as a generalized index of resilience (GIR). We compare the GIR with traditional network indicators and find that it is in certain ways, better.

This paper investigates the process of knowledge exchange in inter-firm Research and Development (R&D) alliances by means of an agent-based model. Extant research has pointed out that firms select alliance partners considering both network-related and network-unrelated features (e.g., social capital versus complementary knowledge stocks). In our agent-based model, firms are located in a metric knowledge space. The interaction rules incorporate an exploration phase and a knowledge transfer phase, during which firms search for a new partner and then evaluate whether they can establish an alliance to exchange their knowledge stocks. The model parameters determining the overall system properties are the rate at which alliances form and dissolve and the agents’ interaction radius. Next, we define a novel indicator of performance, based on the distance traveled by the firms in the knowledge space. Remarkably, we find that — depending on the alliance formation rate and the interaction radius — firms tend to cluster around one or more attractors in the knowledge space, whose position is an emergent property of the system. And, more importantly, we find that there exists an inverted U-shaped dependence of the network performance on both model parameters.