Can Transient Instability Be Used to Accelerate Stochastic State Transitions? A Numerical Investigation of Stability, Mobility, and Recoverability

This preprint investigates whether transient dynamical instability can be deliberately exploited as a mechanism for accelerating stochastic state transitions in a coupled nonlinear system. Using a stochastic radial feedback model coupled to a bistable target process, the study examines how temporary changes in dynamical stability influence stochastic mobility, target-state first-passage times, and the ability of the system to recover its original stable state. The investigation combines analytical characterization of fixed points, local stability multipliers and deterministic basin boundaries with numerical experiments on stochastic escape, noise-dependent transition probabilities, and separatrix scaling. It further examines the relationship between unstable-state exposure and transition acceleration, including matched-diffusion comparisons that identify enhanced diffusion as the proximate mechanism of acceleration in the studied model. The results suggest that transient instability can function as a controllable resource for increasing stochastic transition rates, but that its usefulness is constrained by activation duration, disturbance intensity, and the risk of irreversible escape. This work presents a model-specific numerical investigation of the possibility of using instability constructively, rather than treating instability exclusively as an undesirable dynamical condition. This manuscript is a research preprint and has not undergone peer review.