Abstract
While numerous studies have suggested that large natural, biological, social, and technological networks are fragile, convincing theories are still lacking to explain why natural evolution and human design have failed to optimize networks and avoid fragility. In this paper we provide analytical and numerical evidence that a tradeoff exists in networks with linear dynamics, according to which general measures of robustness and performance are in fact competitive features that cannot be simultaneously optimized. Our findings show that large networks can either be robust to variations of their weights and parameters, or efficient in responding to external stimuli, processing noise, or transmitting information across long distances. As illustrated in our numerical studies, this performance tradeoff seems agnostic to the specific application domain, and in fact it applies to simplified models of ecological, neuronal, and traffic networks.
Highlights
Across diverse scientific disciplines and application domains, complex systems are commonly represented as the dynamic interconnection of nodes and edges, where the interaction pattern among different parts is itself complex and may evolve along with the system dynamics
For networks with linear dynamics, we show that (i) a tradeoff exists between the fragility of a network, as measured by its ability to maintain a stable behavior after a perturbation of its edge weights and interconnection structure, and its performance, as measured by its responsiveness to internal and external stimuli, and that (ii) certain network systems may be tuned to sacrifice their robustness in favor of increased responsiveness and adaptability
We focus on networks with linear dynamics and adopt a metric of fragility that measures the ability of the network to maintain a stable behavior in the face of changes of the edge weights
Summary
Across diverse scientific disciplines and application domains, complex systems are commonly represented as the dynamic interconnection of nodes and edges (namely, networks), where the interaction pattern among different parts is itself complex and may evolve along with the system dynamics. Despite being able to accomplish a rich set of dynamic functions through different nodal and interconnection dynamics, many complex networks exhibit fragile behaviors against relatively small variations of the edge weights and interconnection structure. This is the case in ecological systems, where fragility affects the chance that species can coexist at a stable equilibrium[4] (see Fig. 1). For networks with linear dynamics, we show that (i) a tradeoff exists between the fragility of a network, as measured by its ability to maintain a stable behavior after a perturbation of its edge weights and interconnection structure, and its performance, as measured by its responsiveness to internal and external stimuli, and that (ii) certain network systems may be tuned to sacrifice their robustness in favor of increased responsiveness and adaptability
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