Noise enables conditional recovery from collapse: Probabilistic persistence in threshold-activated systems.

Area of Science:

• Nonlinear dynamics
• Complex systems theory
• Theoretical ecology

Background:

• Deterministic models predict system collapse in threshold-activated scenarios.
• Classical extinction theory often overlooks the stabilizing role of environmental variability.
• Understanding system resilience is crucial for predicting ecological and technological outcomes.

Purpose of the Study:

• To investigate the paradoxical effect of stochasticity on deterministic collapse in threshold-activated systems.
• To explore how environmental noise can alter system dynamics and promote stability.
• To challenge conventional understanding of extinction dynamics in nonlinear systems.

Main Methods:

• Utilized a hybrid logistic-sigmoidal map to model system behavior.
• Applied Lyapunov analysis to assess system stability and divergence.
• Employed quasipotential analysis to understand noise-induced transitions and metastability.

Main Results:

• Demonstrated that weak noise can reverse deterministic collapse, enabling probabilistic recovery from extinction.
• Showcased how noise alters phase-space topology, creating new stable states.
• Identified noise-induced metastability and stochastic robustness not present in deterministic models.

Conclusions:

• Environmental variability can stabilize nonlinear systems, contrary to classical extinction theory.
• Stochasticity plays a crucial role in system resilience and recovery.
• Findings offer a new perspective on system dynamics in the presence of environmental fluctuations.