A Mechanistic Nonlinear Dynamical Framework for Feeling-State Evolution: Bifurcation, Trapped States, and Recovery Thresholds

The Feeling State Framework (FSF) is a mechanistic nonlinear model of affective burden in memory-mediated episodes. It was built to explain how an activated memory can either fade or become self-sustaining after the original stimulus has ended. The model separates three evolving state variables—memory activation, cognitive stability, and feeling burden—from two computed quantities—unresolved conflict and integration openness—and couples them through ordinary differential equations. Under the same parameter values, the model can approach either recovery or a persistent trapped state. Recovery means that memory activation and feeling burden fall to zero. The trapped state maintains high activation and burden. In the phase plane, the stable manifold of a saddle point forms the boundary separating initial conditions that recover from those that become trapped. The quiescent set is a continuous line of equilibria, and its transversely attracting segment constitutes the robust recovered regime. The geometry is therefore more precisely described as coexistence of two attracting invariant regimes rather than standard bistability between two isolated equilibria. Near the inactive equilibrium line, the model yields the analytical local threshold C* = (λ − ε)/(λ + μ), where λ is rumination intensity, μ is integration efficiency, and ε is natural decay. This threshold answers whether a very small reactivation initially grows or fades. It does not determine recovery from an arbitrary finite episode. In the baseline finite-episode protocol, the numerically determined initial cognitive-stability boundary is approximately C0 = 0.73. The model also yields a leading-order conflict-driven target C̄0 ≈ 0.43 for cognitive stability while conflict remains active. In the full numerical model, the trapped node and saddle collide and disappear in a fold bifurcation at μc ≈ 0.56. A sufficiently large increase in integration efficiency can therefore remove the trapped attractor rather than merely weaken it. Simulations show that the recovery boundary persists across the tested parameter settings, that identical initial conditions can have different finite-horizon outcomes when state noise is added near the basin boundary, and that a temporary intervention can succeed early but fail after the trajectory has moved deeper into the trapped basin. Near the fold, survivor-conditioned variance and autocorrelation rise among trajectories that have not escaped. A separate simulate-and-recover study shows that parameter estimation is substantially harder when only downstream feeling burden is observed. FSF does not claim novelty for nonlinearity, bifurcation, alternative attractors, or dynamical modeling of affective disorders in general. Its scoped contribution is the specific combination of self-reinforcing memory activation, endogenous cognitive stability, conflict-mediated construction and dissolution, nonlinear basin geometry, and an analytical local recovery threshold.