Formalization of Mental Disintegration Phenomena Through Dynamical Systems Theory: With Applications to DSM-5-TR Diagnostic Categories

Title: Formalization of Mental Disintegration Phenomena Through Dynamical Systems Theory: With Applications to DSM-5-TR Diagnostic Categories Author: Boris Kriger Information Physics Institute, Gosport, Hampshire, United Kingdom Institute of Integrative and Interdisciplinary Research, Toronto, Canada ORCID: 0009-0001-0034-2903 Description: Dynamical systems theory (DST) has been proposed as a unifying framework for psychiatry, in which the healthy mind is a stable attractor, psychiatric disorders are alternative attractors, and clinical deterioration is a critical transition governed by tipping points, hysteresis, and critical slowing down (Scheffer, Bockting, Borsboom et al., JAMA Psychiatry, 2024). However, the original proposal remains a methodological program: it contains no equations, does not engage with the phenomenological content of specific disorders, and does not address phenomena — anosognosia, the fear of madness, internal resistance, gaslighting, collective madness, punitive psychiatry — that lie outside the scope of existing computational psychiatry paradigms. This article develops a unified mathematical formalism that fills these gaps. Starting from a core stochastic differential equation on a potential landscape, we construct a modular system of coupled models — each with explicit equations, consistent notation, and identified parameters — covering the full trajectory of mental disintegration: erosion of resilience, distortion of perception, the tipping point itself, self-reinforcing symptom feedback, loss of insight (anosognosia as a distance-dependent attractor property), the fear of madness as an autocatalytic destabilizing loop, internal resistance as an energy-depleting restoring force, altered time–space perception, the creativity–madness boundary, social isolation dynamics, gaslighting as targeted resilience destruction, collective phase transitions, evolutionary origins of disorder attractors, the role of religious belief, AI-based monitoring, punitive psychiatry as state-space misclassification, and a dynamical typology of suicidal crises. The gradient assumption is addressed explicitly, with quasipotentials (Freidlin–Wentzell theory) introduced for non-gradient dynamics such as bipolar cycling and OCD oscillations. The framework is situated within the broader computational psychiatry landscape — predictive processing, reinforcement learning, network theory — with critical engagement with the early warning signal debate (Helmich et al., 2024; Smit et al., 2025), distinguishing bifurcation-driven transitions (where critical slowing down applies) from noise-induced barrier crossings (where Kramers' escape rate applies but critical slowing down does not). All predictions are classified by their dependence on the bifurcation assumption. The framework is validated through numerical simulations: phase portraits of the potential landscape, bifurcation diagrams, a stochastic trajectory exhibiting critical slowing down, and an integrated simulation combining depression, social isolation, and declining insight that reproduces the clinically observed pattern of insight peaking before and vanishing after the transition. A measurement mapping table links all model variables to specific EMA items, clinical scales, and digital phenotyping instruments. Eight appendices demonstrate the application of the formalism to DSM-5-TR (APA, 2022) diagnostic categories: schizophrenia spectrum disorders (five-dimensional symptom network), bipolar disorders (three-well potential with sleep feedback), depressive disorders (self-sustaining network with hysteresis), anxiety disorders (threat–arousal loops), trauma- and stressor-related disorders (PTSD as trauma-induced attractor), obsessive-compulsive disorders (limit-cycle model with Hebbian deepening), substance use disorders (tolerance–withdrawal–reward attractor), neurocognitive disorders (irreversible landscape degradation), and personality disorders (attractor topology as trait architecture, with the Alternative DSM-5 Model mapped to landscape parameters). 50 pages, 31 references, 2 figures (4 panels), 3 tables, 8 appendices. LaTeX source and simulation code are available upon request. Keywords: dynamical systems theory · computational psychiatry · tipping points · attractors · resilience · stochastic differential equations · bifurcation theory · quasipotential · critical slowing down · DSM-5-TR · anosognosia · symptom networks · Kramers escape rate · hysteresis · numerical simulation License: CC BY 4.0 Resource type: Preprint Subjects: Psychiatry, Computational Neuroscience, Dynamical Systems, Mathematical Biology, Clinical Psychology Related identifiers: Scheffer, M. et al. (2024). A dynamical systems view of psychiatric disorders — Theory. JAMA Psychiatry, 81(6), 618–623. (Is supplemented by this upload) Scheffer, M. et al. (2024). A dynamical systems view of psychiatric disorders — Practical implications. JAMA Psychiatry, 81(6), 624–630. (Is supplemented by this upload)