A 15‑dimensional dynamical system with three well‑separated timescales is reduced, via geometric singular perturbation theory and center manifold reduction, to a one‑dimensional core exhibiting saddle‑node bifurcations. The model incorporates fast neural population dynamics (thalamus, amygdala, prefrontal cortex), fast dopamine clearance, slower serotonin and norepinephrine turnover, and very slow Hebbian plasticity gated by neuromodulator‑selective pathways. The bifurcation analysis partitions the effective emotional arousal into four regimes: hypo‑arousal rigidity, a bistable window of cognitive flexibility, critical transition points, and hyper‑arousal rigidity. Hysteresis is inherent, explaining why reducing arousal alone often fails to restore flexibility. Three experimentally testable predictions are derived analytically: a sharp prefrontal jump at the critical threshold, critical slowing down with recovery time scaling as the inverse square root of the distance to the bifurcation, and accelerated synaptic consolidation under hyper‑arousal due to simultaneous saturation of neural activity and neuromodulatory gating. The persistence of these scaling laws under stochastic noise, slow adaptation, and sigmoidal nonlinearities is demonstrated numerically. The work provides a mechanistic framework for arousal‑dependent cognitive rigidity in psychiatric disorders and a biologically grounded blueprint for continual‑learning architectures that avoid catastrophic forgetting.
Md Labib Sazal (2026) studied this question.