In PT-symmetric rock-paper-scissors and Lotka-Volterra models, exceptional points in the linearization at coexistence coincide with abrupt global destabilization only when the PT symmetry is global, not merely local.
The behavior of the system is visualized in the 3- simplex in the right column of Fig
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Exceptional Points and Stability in Nonlinear Models of Population Dynamics having $\mathcal{PT}$ symmetry
In PT-symmetric rock-paper-scissors and Lotka-Volterra models, exceptional points in the linearization at coexistence coincide with abrupt global destabilization only when the PT symmetry is global, not merely local.