Parameter Space and Model Families in Subjective Field Theory: Structural Stability of Nonlinear Regime Dynamics in Psychotherapy

Psychotherapeutic processes are often modeled using fixed-parameter formulations, raising concerns about arbitrariness and sensitivity to parameter selection. The present study addresses this limitation by reformulating Subjective Field Theory (SFT) as a family of parametrized nonlinear dynamical systems defined over a structured parameter space. A key innovation introduced in recent extensions of SFT is the coupling between symbolic weight (Wₚ) and transition sharpness, expressed as βeff = β₀·exp(−γ·Wₚ). Rather than evaluating a single model instantiation, we analyze the qualitative behavior of the system under local exploration of four key parameters: affective-temporal decay (λ), symbolic weight gain (α), baseline threshold steepness (β₀), and symbolic sensitivity (γ). Using simulated cases representing canonical regime configurations—capacity-dominant, load-dominant, oscillatory threshold, and transitional—we demonstrate that qualitative regime structure remains invariant across a neighborhood of parameter space. While parameter variation modulates amplitude, sensitivity, and transition sharpness, it does not alter regime classification or the presence of threshold-mediated dynamics. These findings support the interpretation of SFT as a structurally stable dynamical framework in which regime configurations emerge as intrinsic properties of the model architecture rather than artifacts of parameter tuning. By shifting the focus from parameter instantiation to model families, the present work establishes a formal foundation for robust and interpretable modeling of psychotherapy processes grounded in nonlinear dynamics.