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This paper introduces "quasi-narcissistic dynamics" — a term emphasizing that the phenomena conventionally attributed to narcissistic personality disorder are not consequences of a diagnosis but emergent properties of a general dynamical systems class. We formalize this claim by developing a rigorous mathematical framework for asymmetric relational exploitation, modeled as a coupled two-agent dynamical system with asymmetric utility functions, information channel distortion, and positive feedback stabilization. The key results include: Axiomatic derivation of agent utility functions from four behavioral primitives, with robustness verification under nonlinear transformations. A complete asymmetric bimatrix game with proved Nash equilibrium existence and uniqueness. Proof that the characteristic idealization–devaluation cycle emerges as a stable limit cycle via the Poincaré–Bendixson theorem, with explicit trapping region construction and period formula. A Bayesian persuasion model of gaslighting (epistemic degradation) demonstrating a sharp phase transition in victim autonomy, with Hoeffding concentration bounds. Formal derivation of victim entrenchment from three coupled positive feedback loops: sunk-cost-weighted dissonance resolution, autocatalytic precision erosion, and informational isolation. Extension to symmetric exploitation (two coupled quasi-narcissistic oscillators), predicting three dynamical regimes: in-phase synchronization, anti-phase synchronization, and deterministic chaos. Replicator dynamics showing conditions under which quasi-narcissistic strategies invade cooperative populations. Three novel, empirically testable predictions with explicit falsification criteria. The paper demonstrates that the identical mathematical structure manifests in authoritarian political systems, cults, toxic corporate leadership, addictive dynamics, algorithmic attention platforms, asymmetric international relations, and exploitative professional relationships. A formal structural isomorphism with a thermostat control system (Appendix A) and a general definition of the dynamical systems class (Kriger systems, Definition I.1) establish that the dynamics are substrate-independent. The central thesis: the diagnostic category "narcissist" is unnecessary for explanation, prediction, or intervention. The label is shown to be not only redundant but actively harmful — satisfying all five structural conditions of the very mechanism it purports to describe. The dynamics suffice.
Kriger B. 2026. Extractive Oscillators with Sensor Degradation: A Dynamical Systems Class and Its Manifestation in Quasi-Narcissistic Relational Dynamics. PREPRINTS.RU. https://doi.org/10.24108/preprints-3115649
