Emergent non-Hermitian physics in generalized Lotka-Volterra model

TL;DR

This paper explores how non-Hermitian physics emerges in a generalized Lotka-Volterra predator-prey model, revealing phase transitions between chaotic and localized dynamics linked to exceptional points.

Contribution

It demonstrates the emergence of non-Hermitian phenomena, including exceptional points, within a nonlinear ecological model, connecting ecological dynamics with non-Hermitian physics.

Findings

Chaotic and localized dynamics separated by a critical point.

Dynamics at the critical point exhibit algebraic divergence.

Effective Hamiltonian exhibits non-Hermiticity and exceptional points.

Abstract

In this paper, we study the non-Hermitian physics emerging from a predator-prey ecological model described by a generalized Lotka-Volterra equation. In the phase space, this nonlinear equation exhibits both chaotic and localized dynamics, which are separated by a critical point. These distinct dynamics originate from the interplay between the periodicity and non-Hermiticity of the effective Hamiltonian in the linearized equation of motion. Moreover, the dynamics at the critical point, such as algebraic divergence, can be understood as an exceptional point in the context of non-Hermitian physics.