Robustness Of Complex Systems Research Articles

Oscillatory network spontaneously recovers both activity and robustness after prolonged removal of neuromodulators.

Robustness of neuronal activity is a property necessary for a neuronal network to withstand perturbations, which may otherwise disrupt or destroy the system. The robustness of complex systems has been shown to depend on a number of features of the system, including morphology and heterogeneity of the activity of the component neurons, size of the networks, synaptic connectivity, and neuromodulation. The activity of small networks, such as the pyloric network of the crustacean stomatogastric nervous system, appears to be robust despite some of the factors not being consistent with the expected properties of complex systems, e.g., small size and homogeneity of the synaptic connections. The activity of the pyloric network has been shown to be stable and robust in a neuromodulatory state-dependent manner. When neuromodulatory inputs are severed, activity is initially disrupted, losing both stability and robustness. Over the long term, however, stable activity homeostatically recovers without the restoration of neuromodulatory input. The question we address in this study is whether robustness can also be restored as the network reorganizes itself to compensate for the loss of neuromodulatory input and recovers the lost activity. Here, we use temperature changes as a perturbation to probe the robustness of the network's activity. We develop a simple metric of robustness, i.e., the variances of the network phase relationships, and show that robustness is indeed restored simultaneously along with its stable network activity, indicating that, whatever the reorganization of the network entails, it is deep enough also to restore this important property.

Higher-order interdependent percolation on hypergraphs

A fundamental concern on the robustness of hypergraphs lies in comprehending how the failure of individual nodes affects the hyperedges they are associated with. To address the issue, we propose a simple but novel percolation model that takes into account the dependency of hyperedges on their internal nodes, where the failure of a single node can lead to the dissolution of its associated hyperedge with a probability β. Based on a newly proposed analytical method of percolation theory on hypergraphs, our research reveals that the impact of mean cardinality on the system robustness varies with β. For a large value of β, a larger mean cardinality increases the fragility of hypergraphs, while for a small β, a larger mean cardinality enhances the robustness of hypergraphs. Additionally, our research uncovers divergent effects of hyperdegree distribution on system robustness between monolayer and double-layer hypergraphs. Specifically, monolayer hypergraphs with scale-free hyperdegree distribution exhibit higher robustness, while Poisson hyperdegree distributions lead to stronger robustness in double-layer hypergraphs. These findings provide valuable insights into the robustness of hypergraphs and its dependency on hyperdegree distributions and mean cardinality, contributing to a more comprehensive understanding of the complexities of robustness in complex systems. Furthermore, the development of the percolation model enriches our understanding of node-hyperedge interactions within complex systems.

Percolation Theories for Multipartite Networked Systems under Random Failures

Real-world complex systems inevitably suffer from perturbations. When some system components break down and trigger cascading failures on a system, the system will be out of control. In order to assess the tolerance of complex systems to perturbations, an effective way is to model a system as a network composed of nodes and edges and then carry out network robustness analysis. Percolation theories have proven as one of the most effective ways for assessing the robustness of complex systems. However, existing percolation theories are mainly for multilayer or interdependent networked systems, while little attention is paid to complex systems that are modeled as multipartite networks. This paper fills this void by establishing the percolation theories for multipartite networked systems under random failures. To achieve this goal, this paper first establishes two network models to describe how cascading failures propagate on multipartite networks subject to random node failures. Afterward, this paper adopts the largest connected component concept to quantify the networks’ robustness. Finally, this paper develops the corresponding percolation theories based on the developed network models. Simulations on computer-generated multipartite networks demonstrate that the proposed percolation theories coincide quite well with the simulations.

Generalized network dismantling

Finding an optimal subset of nodes in a network that is able to efficiently disrupt the functioning of a corrupt or criminal organization or contain an epidemic or the spread of misinformation is a highly relevant problem of network science. In this paper, we address the generalized network-dismantling problem, which aims at finding a set of nodes whose removal from the network results in the fragmentation of the network into subcritical network components at minimal overall cost. Compared with previous formulations, we allow the costs of node removals to take arbitrary nonnegative real values, which may depend on topological properties such as node centrality or on nontopological features such as the price or protection level of a node. Interestingly, we show that nonunit costs imply a significantly different dismantling strategy. To solve this optimization problem, we propose a method which is based on the spectral properties of a node-weighted Laplacian operator and combine it with a fine-tuning mechanism related to the weighted vertex cover problem. The proposed method is applicable to large-scale networks with millions of nodes. It outperforms current state-of-the-art methods and opens more directions for understanding the vulnerability and robustness of complex systems.

Self-Organization, Resilience and Robustness of Complex Systems Through an Application to Financial Market from an Agent-Based Approach

This paper introduces the implementation of a computational agent-based financial market model in which the system is described on both microscopic and macroscopic levels. This artificial financial market model is used to study the system response when a shock occurs. Indeed, when a market experiences perturbations, financial systems behavior can exhibit two different properties: resilience and robustness. Through simulations and different scenarios of market shocks, these system properties are studied. The results notably show that the emergence of collective herding behavior when market shock occurs leads to a temporary disruption of the system self-organization. Numerical simulations highlight that the market can absorb strong mono-shocks but can also be led to rupture by low but repeated perturbations.

Stability threshold approach for complex dynamical systems

A new measure to characterize the stability of complex dynamical systems against large perturbations is suggested, the stability threshold (ST). It quantifies the magnitude of the weakest perturbation capable of disrupting the system and switch it to an undesired dynamical regime. In the phase space, the ST corresponds to the ‘thinnest site’ of the attraction basin and therefore indicates the most ‘dangerous’ direction of perturbations. We introduce a computational algorithm for quantification of the ST and demonstrate that the suggested approach is effective and provides important insights. The generality of the obtained results defines their vast potential for application in such fields as engineering, neuroscience, power grids, Earth science and many others where the robustness of complex systems is studied.

Degeneracy and long-range correlation: A simulation study

We present in this paper a simulation study that aimed at evidencing a causal relationship between degeneracy and long-range correlations. Long-range correlations represent a very specific form of fluctuations that have been evidenced in the outcomes time series produced by a number of natural systems. Long-range correlations are supposed to sign the complexity, adaptability and flexibility of the system. Degeneracy is defined as the ability of elements that are structurally different to perform the same function, and is presented as a key feature for explaining the robustness of complex systems. We propose a model able to generate long-range correlated series, and including a parameter that account for degeneracy. Results show that a decrease in degeneracy tends to reduce the strength of long-range correlation in the series produced by the model.

Distributed redundancy and robustness in complex systems

The uptake and increasing prevalence of Web 2.0 applications, promoting new large-scale and complex systems such as Cloud computing and the emerging Internet of Services/Things, requires tools and techniques to analyse and model methods to ensure the robustness of these new systems. This paper reports on assessing and improving complex system resilience using distributed redundancy, termed degeneracy in biological systems, to endow large-scale complicated computer systems with the same robustness that emerges in complex biological and natural systems. However, in order to promote an evolutionary approach, through emergent self-organisation, it is necessary to specify the systems in an ‘open-ended’ manner where not all states of the system are prescribed at design-time. In particular an observer system is used to select robust topologies, within system components, based on a measurement of the first non-zero Eigen value in the Laplacian spectrum of the components' network graphs; also known as the algebraic connectivity. It is shown, through experimentation on a simulation, that increasing the average algebraic connectivity across the components, in a network, leads to an increase in the variety of individual components termed distributed redundancy; the capacity for structurally distinct components to perform an identical function in a particular context. The results are applied to a specific application where active clustering of like services is used to aid load balancing in a highly distributed network. Using the described procedure is shown to improve performance and distribute redundancy.

Robustness in complex information systems: The role of information “barriers” in Boolean networks

AbstractIn this supposed “information age,” a high premium is put on the widespread availability of information. Access to as much information as possible is often cited as key to the making of effective decisions. While it would be foolish to deny the central role that information and its flow has in effective decision‐making processes, this chapter explores the equally important role of “barriers” to information flows in the robustness of complex systems. The analysis demonstrates that (for simple Boolean networks at least) a complex system's ability to filter out, i.e., block, certain information flows is essential if it is not to be beholden to every external signal. The reduction of information is as important as the availability of information. © 2009 Wiley Periodicals, Inc. Complexity, 2010

Managing Complexity in Socio-Economic Systems

This contribution summarizes some typical features of complex systems such as non-linear interactions, chaotic dynamics, the ``butterfly effect’’, phase transitions, self-organized criticality, cascading effects, and power laws. These imply sometimes quite unexpected, counter-intuitive, or even paradoxical behaviors of socio-economic systems. A typical example is the faster-is-slower effect. Due to their tendency of self-organization, complex systems are often hard to control. Instead of trying to control their behavior, it would often be better to pursue the approach of guided self-organization, i.e. to use the driving forces of the system rather than to fight against them. This is illustrated by the example of hierarchical systems, which need to fulfill certain principles in order to be efficient and robust in an ever-changing environment. We also discuss the important role of fluctuations and heterogeneity for the adaptability, flexibility and robustness of complex systems. The presentation is enriched by a number of examples ranging from decision behavior up to production systems and disaster spreading.