Emergence of Network Bifurcation Triggered by Entanglement
Xi Yong, Man-Hong Yung, Xue-Ke Song, Xun Gao, Angsheng Li

TL;DR
This paper uncovers a new bifurcation mechanism in anti-symmetric Lotka-Volterra systems, where quantum entanglement triggers abrupt changes in equilibrium states, with implications for physical and evolutionary networks.
Contribution
It introduces a novel bifurcation mechanism in ALV equations driven by quantum entanglement, linking microscopic quantum effects to macroscopic network dynamics.
Findings
Bifurcation can be triggered by entanglement exceeding a critical value.
The bifurcation mechanism is robust across different network topologies.
Theoretical predictions of critical entanglement values match numerical results.
Abstract
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…
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