  Studies of topological bands and their associated low-dimensional boundary
modes have largely focused on linear systems. This work reports robust
dynamical features of three-dimensional (3D) nonlinear systems in connection
with intriguing topological bands in 3D. Specifically, for a 3D setting of
coupled rock-paper-scissors cycles governed by the antisymmetric Lotka-Volterra
equation (ALVE) that is inherently nonlinear, we unveil distinct
characteristics and robustness of surface polarized masses and analyze them in
connection with the dynamics and topological bands of the linearized
Lotka-Volterra (LV) equation. Our analysis indicated that insights learned from
Weyl semimetal phases with type-I and type-II Weyl singularities based on a
linearized version of the ALVE are still remarkably useful, even though the
system dynamics is far beyond the linear regime. This work indicates the
relevance and importance of the concept of topological boundary modes in
analyzing high-dimensional nonlinear systems and hopes to stimulate another
wave of topological studies in nonlinear systems.
