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

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.
Comment: 9 pages, 7 figures