Stability and performance of complex systems under external perturbation have long been studied, and both diversity theory and the May-Wigner theorem are two widely acknowledged approaches to such studies. Diversity theory emphasizes the important role of differences among individuals for a system to be resilient and survive in dynamic environments. However, the May-Wigner theorem suggests that the similarity between individuals can make a system more robust against external perturbations. The conflicting conclusions of diversity theory and the May-Wigner theorem might suggest there is a missing link. Here we propose a new fundamental network property, concilience degree, which quantitatively evaluates the functional fusion of topology and node activities in a network system. Based on the concept of concilience degree, simulation results imply that:
– The May-Wigner Theorem emphasizes short-term system performance, at the cost of potentially reducing longer-term system stability.
– Diversity theory on the other hand emphasizes system stability on long timescales, while the performance of a diversified system may be poor.
– Based on diversified node activity states, the concilience approach can achieve stability and good performance both on a shorter and a longer timescale.


Xiao-Bing Hu

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