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Noise enables conditional recovery from collapse: Probabilistic persistence in threshold-activated systems
Vinesh Vijayan1, B Priyadharshini1, R Sathish Kumar1
1Department of Science and Humanities, Rathinam Technical Campus, Coimbatore 641021, India.
Abstract:
We report a paradoxical phenomenon where stochasticity reverses deterministic collapse in threshold-activated systems. By using a hybrid logistic-sigmoidal map, we show that weak noise alters phase-space topology, enabling probabilistic recovery from extinction. Lyapunov and quasipotential analyses reveal noise-induced metastability and stochastic robustness absent in deterministic frameworks. These results suggest that environmental variability can stabilize nonlinear systems, offering a counternarrative to classical extinction theory.
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