Topological phase transition in anti-symmetric Lotka-Volterra doublet chain

TL;DR

This paper demonstrates a topological phase transition in a minimal two-dimensional rock-paper-scissors model, showing edge-localized mass transfer and robustness characteristic of topological phases, confirmed via topological band theory.

Contribution

It introduces a topological phase transition in an anti-symmetric Lotka-Volterra doublet chain, linking ecological dynamics with topological band theory.

Findings

Mass decays exponentially towards edges, indicating topological edge states.

Winding number changes from zero to one, confirming a topological phase transition.

Bulk remains gaped in the non-trivial phase.

Abstract

We present the emergence of topological phase transition in the minimal model of two dimensional rock-paper-scissors cycle in the form of a doublet chain. The evolutionary dynamics of the doublet chain is obtained by solving the anti-symmetric Lotka-Volterra equation. We show that the mass decays exponentially towards edges and robust against small perturbation in the rate of change of mass transfer, a signature of a topological phase. For one of the configuration of our doublet chain, the mass is transferred towards both edges and the bulk is gaped. Further, we confirm this phase transition within the framework of topological band theory. For this we calculate the winding number which change from zero to one for trivial and a non-trivial topological phases respectively.