Do Connections Make Systems Robust? A New Scenario for the Complexity-Stability Relation

Whether interactions among the elements make the system robust or fragile has been a central issue in broad range of field. Here we introduce a novel type of mechanism which governs the robustness of open and dynamical systems such as social and economical systems, based on a very simple mathematical model. This mechanism suggest a moderate number ( ∼ 10) of interactions per element is optimal to make the system against successive and unpredictable disturbances. The relation between this very simple model and more detailed nonlinear dynamical models is discussed, to emphasize the relevance of this newly reported mechanism to the real phenomena.

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