Schizophrenia (SCZ), bipolar disorder (BD), and major depressive disorder (MDD) are associated with structural brain abnormalities. Lyapunov-based approaches may provide additional descriptors of nonlinear gray-matter (GM) organization that might not be reflected by standard morphometric metrics. This study examined whether nonlinear GM topology differs between SCZ, BD, MDD, and healthy controls (HC). Structural T1-weighted MRI data from 161 participants (HC = 53, MDD = 67, BD = 25, SCZ = 16) were analyzed. Images were preprocessed in CAT12/SPM12, and subject-specific one-dimensional spatial sequences were derived from modulated and normalized GM maps by multiplying voxel intensity with Euclidean distance from the individual GM center of mass. The 5000 highest spatially weighted GM values were ranked in descending order and submitted to a Rosenstein-based Lyapunov analysis. Two Lyapunov-based outputs, largest Lyapunov exponent (LLE) and Lambda (λ), were computed and projected back into three-dimensional brain space and analyzed using voxel-wise analysis of covariance. Significant group differences were observed in both nonlinear outputs. BD showed lower nonlinear values than HC and MDD in the right cerebellum. SCZ showed lower nonlinear values than HC and MDD in the left lingual gyrus. BD showed higher values than SCZ in the same lingual region. No significant differences were observed between MDD and HC. The spatial pattern was identical for LLE and Lambda. Lyapunov-based structural MRI topology analysis revealed disorder-specific alterations in nonlinear GM organization. BD was primarily associated with cerebellar alterations, and SCZ with deviations in the lingual gyrus. These findings support the utility of nonlinear structural descriptors for characterizing GM topology across major psychiatric disorders. Replication in larger and clinically well-characterized cohorts with more balanced sample sizes across diagnostic groups is required.