Extinction transitions in correlated external noise.

Area of Science:

• Physics
• Ecology
• Complex Systems

Background:

• Environmental noise, or temporal disorder, can lead to unusual critical points in population dynamics.
• Previous research identified an "infinite-noise" critical point characterized by extreme density fluctuations.

Purpose of the Study:

• To investigate the influence of long-range correlated (colored) noise on extinction phase transitions.
• To analyze how correlated noise modifies population decay dynamics compared to uncorrelated noise.

Main Methods:

• Analysis of the logistic evolution equation.
• Establishment of a connection to fractional random walks.
• Extensive Monte Carlo simulations.

Main Results:

• Positively correlated (red) noise enhances density fluctuations and accelerates the decay of typical populations.
• Correlated noise slows the decay of the ensemble average, which is influenced by rare, surviving events.
• The mean time to extinction grows sub-power-law with population size in the surviving phase.

Conclusions:

• Correlated environmental noise significantly alters extinction transition dynamics, leading to divergent behaviors between typical and average population fates.
• The study connects extinction transitions to fractional random walks, providing a theoretical framework for understanding these phenomena.
• Findings have implications for modeling population dynamics in environments with temporally structured noise.