Uncertainty quantification of multi-scale resilience in networked systems with nonlinear dynamics using arbitrary polynomial chaos

Abstract

Complex systems derive sophisticated behavioral dynamics by connecting individual component dynamics via a complex network. The resilience of complex systems is a critical ability to regain desirable behavior after perturbations. In the past years, our understanding of large-scale networked resilience is largely confined to proprietary agent-based simulations or topological analysis of graphs. However, we know the dynamics and topology both matter and the impact of model uncertainty of the system remains unsolved, especially on individual nodes. In order to quantify the effect of uncertainty on resilience across the network resolutions (from macro-scale network statistics to individual node dynamics), we employ an arbitrary polynomial chaos (aPC) expansion method to identify the probability of a node in losing its resilience and how the different model parameters contribute to this risk on a single node. We test this using both a generic networked bi-stable system and also established ecological and work force commuter network dynamics to demonstrate applicability. This framework will aid practitioners to both understand macro-scale behavior and make micro-scale interventions.

Advanced progress of network resilience

“…They estimated resilience behavior in large-scale network systems and analyzed the influence of topological and dynamic parameters. Zou et al [71] used the arbitrary polynomial chaos expansion method to quantify uncertainty in nodes and analyze the influence of uncertainty parameters on resilience.…”

“…t 0 denotes the initial time of pre-disturbance phase. The [71] Network resilience in network dynamics with uncertainty.…”

Resilience and Complex Dynamics — Safeguarding Local Stability Against Global Instability

“…The attractor of the dynamical system is reconstructed using Takens embedding rule and singular value decomposition Takens (1981). Notice that "the resilience of complex systems is a critical ability to regain desirable behavior after perturbations" (Zou et al 2023), the presence of an attractor ensures the said resilience at least within a given domain. In terms of empirical tests, business cycles versus the model proposed in system (17) have been extensively investigated through recurrence quantification analysis (RQA) Marwan et al (2007), , principal component analysis (PCA) and Poincaré Plot with related quantifiers.…”