Antifragility is a property from which systems are able to resist stress and furthermore benefit from it. Even though antifragile dynamics is found in various real-world complex systems where multiple subsystems interact with each other, the attribute has not been quantitatively explored yet in those complex systems which can be regarded as multilayer networks. Here we study how the multilayer structure affects the antifragility of the whole system. By comparing single-layer and multilayer Boolean networks based on our recently proposed antifragility (...) measure, we found that the multilayer structure facilitated the production of antifragile systems. Our measure and findings will be useful for various applications such as exploring properties of biological systems with multilayer structures and creating more antifragile engineered systems. (shrink)

The σ profile is presented as a tool to analyze the organization of systems at different scales, and how this organization changes in time. Describing structures at different scales as goal‐oriented agents, one can define σ ∈ [0,1] (satisfaction) as the degree to which the goals of each agent at each scale have been met. σ reflects the organization degree at that scale. The σ profile of a system shows the satisfaction at different scales, with the possibility to study their (...) dependencies and evolution. It can also be used to extend game theoretic models. The description of a general tendency on the evolution of complexity and cooperation naturally follows from the σ profile. Experiments on a virtual ecosystem are used as illustration. (shrink)