High-dimensional amplitude death induced by matrix frustration

Frustration is widespread in coupled systems and can substantially reshape their collective dynamics. Previous studies incorporated phase frustration into high-dimensional spherical oscillators through a coupling matrix while keeping the amplitude fixed. We introduce matrix-frustrated coupling into high-dimensional generalized limit-cycle oscillators and examine the resulting amplitude-death states. In homogeneous populations, the matrix-frustration parameters, including the phase offset 𝛼 , directly shift the amplitude-death boundary. Frequency heterogeneity then separates the odd- and even-dimensional responses and qualitatively changes the role of frustration: as heterogeneity strengthens and a heterogeneity-controlled branch becomes dominant, the boundary loses its leading dependence on 𝛼 . For isotropically heterogeneous odd-dimensional populations, the death interval is governed mainly by the axial parameter 𝛽 and depends only weakly on the phase offset 𝛼 . The even-dimensional block response has no axial parameter, and strong heterogeneity makes its death boundary nearly independent of 𝛼 . Increasing the intrinsic-amplitude parameter 𝜇 shifts the boundary to stronger coupling and contracts the death region. Linear stability and mean-field resolvent analyses yield the amplitude-death boundaries and identify the roles of matrix frustration, intrinsic amplitude, and frequency heterogeneity.