Emergence of Network Bifurcation Triggered by Entanglement

Xi Yong1,2,3, Man-Hong Yung4,5,6,7, Xue-Ke Song4,5,8, Xun Gao6, and Angsheng Li1

1State Key Laboratory of Computer Science, Institute of Software, Chinese Academy of Sciences, P. R. China
2University of Chinese Academy of Sciences, P. R. China
3Water Information Center, Ministry of Water Resources, Beijing 100053, P. R. China
4Institute for Quantum Science and Engineering and Department of Physics, Southern University of Science and Technology, Shenzhen 518055, P. R. China
5Shenzhen Key Laboratory of Quantum Science and Engineering, Shenzhen 518055, P. R. China
6Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, P. R. China
7Central Research Institute, Huawei Technologies, Shenzhen 518129, P. R. China
8Department of Physics, Southeast University, Nanjing 211189, P. R. China

In many non-linear systems, such as plasma oscillation, boson condensation, chemical reaction, and even predatory-prey oscillation, the coarse-grained dynamics are governed by an equation containing anti-symmetric transitions, known as the anti-symmetric Lotka-Volterra (ALV) equations. In this work, we prove the existence of a novel bifurcation mechanism for the ALV equations, where the equilibrium state can be drastically changed by flipping the stability of a pair of fixed points. As an application, we focus on the implications of the bifurcation mechanism for evolutionary networks; we found that the bifurcation point can be determined quantitatively by the microscopic quantum entanglement. The equilibrium state can be critically changed from one type of global demographic condensation to another state that supports global cooperation for homogeneous networks. In other words, our results indicate that there exist a class of many-body systems where the macroscopic properties are invariant with a certain amount of microscopic entanglement, but they can be changed abruptly once the entanglement exceeds a critical value. Furthermore, we provide numerical evidence showing that the emergence of bifurcation is robust against the change of the network topologies, and the critical values are in good agreement with our theoretical prediction. These results show that the bifurcation mechanism could be ubiquitous in many physical systems, in addition to evolutionary networks.

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