Effective-frequency shear organizes chaotic response under higher-order coupling

Abstract

How higher-order interactions reorganize chaotic responses beyond established coherence-based descriptions remains incompletely resolved. In amplitude-active systems, such responses are often interpreted through phase coherence, although coherence alone does not determine collective instability. Here we study a minimal globally coupled quartet of nonisochronous Stuart--Landau oscillators with pairwise and symmetric three-body interactions. Because the pairwise system already supports a connected chaotic branch, the higher-order channel reconstructs rather than creates irregular dynamics. We show that this reconstruction is organized more directly by effective-frequency shear than by phase coherence. Higher-order coupling regulates amplitude heterogeneity, nonisochronicity converts it into differential angular velocities, and the resulting shear structures the Lyapunov response. This reduced shear-based description reveals an indirect amplitude--shear pathway for higher-order control of chaotic dynamics.