Topological phase transition in coupled rock-paper-scissor cycles

TL;DR

This paper uncovers topological phases in a nonlinear system modeling rock-paper-scissors dynamics, revealing boundary modes, polarization states, and solitonic waves at phase transitions, linking biological cycles to topological physics.

Contribution

It demonstrates topological phases in the antisymmetric Lotka-Volterra equation, a nonlinear model of evolutionary dynamics, connecting biological cycles to topological classification.

Findings

Topological phases manifest as polarization states in the system.

Solitonic waves occur at the transition between polarization states.

The phase transition belongs to symmetry class D, similar to 1D topological superconductors.

Abstract

A hallmark of topological phases is the occurrence of topologically protected modes at the system`s boundary. Here we find topological phases in the antisymmetric Lotka-Volterra equation (ALVE). The ALVE is a nonlinear dynamical system and describes, e.g., the evolutionary dynamics of a rock-paper-scissors cycle. On a one-dimensional chain of rock-paper-scissor cycles, topological phases become manifest as robust polarization states. At the transition point between left and right polarization, solitonic waves are observed. This topological phase transition lies in symmetry class $D$ within the "ten-fold way" classification as also realized by 1D topological superconductors.