Emergence of Network Bifurcation Triggered by Entanglement

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 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.