Are Complex Systems Unstable?
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Sitabhra Sinha
Faculty Member of the Theoretical Physics Group, Institute of Mathematical Sciences, Chennai, India
Are Complex Systems Unstable?
Is a large inter-connected network of elements (e.g., power grids, ecologies, computer networks) more stable or less stable to perturbations as more and more elements are added to it? Results based on random matrix theory due to Wigner & May, seem to suggest that complexity implies fragility in a large network. This runs counter to many empirical studies which claim that diversity is essential for stability, and has led to the famous complexity vs. stability debate in ecology. We have shown that the two main objections against the May-Wigner argument, namely, (i) it is based on local stability and (ii) it is only valid for random networks, are not tenable and that the original May-Wigner result may be universally applicable to networks. We also show that, in the specific context of a network assembly model, the apparently contradictory claims of the opposing groups in the complexity vs. stability debate can be resolved. Further, we find that imposing certain structural and resource constraints (together with the requirement of dynamical stability) results in the emergence of modular structures.