The Strong Reinforcement Effects of Bidirectionality of Interactions on the Robustness of Evolving Open Systems

The robustness against inclusion of new elements is an essential feature of diverse kinds of real complex systems such as living organisms, ecosystems, social and economic systems, and complex engineering system with bottom-up design principle. A recently proposed simple model has revealed a general mechanism of determining the robustness of such systems against inclusion of elements with totally random interactions [1]. Under this mechanism, the system can grow only if the connection is moderately sparse.
The interaction in many real systems, however, often has intrinsically bidirectional nature like mutual symbiosis, predation, and competition in ecology. In this talk we report the strong reinforcement effect of the bidirectionality of the interactions on the robustness of evolving systems [2]. We show that the system with bidirectional interactions can grow with about twofold average degree, in comparison with the purely unidirectional system. This drastic change stems from a slight reinforcement effect of each node, not from the emergence of any prominent structuring. We will also show that for systems with partially bidirectional interactions the regime of the growing phase gets expanded. And in the dense interaction regime, there exists an optimum proportion of bidirectional interactions for the growth rate at around 1/3. The effect of other correlations in interaction, such as mutuality and preferential attachment, will be also discussed.

Authors: 
Takashi Shimada, Fumiko Ogushi, Kimmo Kaski and Janos Kertesz
Room: 
2
Date: 
Monday, September 24, 2018 - 17:45 to 18:00

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