Takashi Shimada (Department of Applied Physics, The University of Tokyo)

Monday 2016-08-01 11.00 – 12.00

Lecture hall AS3, TUAS building

## A transition in growth and robustness of evolving networks

An important and universal feature of real complex systems, such as social, economic, engineering, ecological, and biological systems, is that those are open: in those systems, constituting elements are not fixed and the complexity emerges (at least persist) under successive introductions of new elements. Those systems sometimes grow, but also sometimes collapse. Therefore why and when, in general, we can have such open and complex systems is a fundamental question. In this talk, we revisit this classical problem using our very simple graph dynamics model. I will show that this model gives either continuous growth or stagnation in system size, depending on the model’s unique parameter: the average number of weighted links per node m. The system can grow only if the connection is moderately sparse, i.e. 5 m 18. We can further find that this transition originates from an essential balance of two effects: although having more interactions makes each node robust, it also increases the impact of the loss of a node [1, 2]. This novel relation might be a origin of the moderately sparse (average degree 10) network structure ubiquitously found in real world, and the non-trivial distribution function of the lifetime of elements [3].

[1] T. Shimada, in Springer monograph Mathematical Approaches to Biological Systems: networks, Oscillations and Collective Motions (Springer, 2015) p. 95-117.

[2] T. Shimada “ A universal transition in the robustness of evolving open systems ”, Scientific Reports Vol. 4, 4082 (2014).

[3] Y. Murase, T. Shimada, & Ito, N.“A simple model for skewed species-lifetime distributions ”, New J. of Physics 12, 063021 (2010).