The Stochastic Gause Predator-Prey model: Noise-induced extinctions and invariance

Sanchéz, Andrés Jorge; Valencia, Leon Alexander; Osorio, Jorge M. Ramirez

doi:10.3934/mbe.2025073

The Stochastic Gause Predator-Prey model: Noise-induced extinctions and invariance

Journal Article · Thu Jun 26 00:00:00 EDT 2025 · Mathematical Biosciences and Engineering

DOI:https://doi.org/10.3934/mbe.2025073· OSTI ID:3002779

Sanchéz, Andrés Jorge ^[1]; Valencia, Leon Alexander ^[1]; ^[2]

Universidad de Antioquia, Medellín (Colombia)
Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States)

We consider the Gause predator-prey with general bounded or sub‑linear functional responses, – which includes those of Holling types Ⅰ–Ⅳ. – and multiplicative Gaussian noise. In contrast to previous studies, the prey in our model follows logistic dynamics while the predator's population is solely regulated by consumption of the prey. To ensure well-posedeness, we derive explicit Lyapunov‐type criteria ensuring global positivity and moment boundedness of solutions. We find conditions for noise‑induced extinctions, proving that stochasticity can drive either population to collapse even when the deterministic analogue predicts stable coexistence. In the case when the predator becomes extinct, we establish a limiting distribution for the predator's population. Last, for functional responses of Holling type Ⅰ, we provide sufficient conditions on the intensity of the noise for the existence and uniqueness of a stationary distribution.

Research Organization:: Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States)

Sponsoring Organization:: USDOE Office of Science (SC); USDOE Laboratory Directed Research and Development (LDRD) Program

Grant/Contract Number:: AC05-00OR22725

OSTI ID:: 3002779

Journal Information:: Mathematical Biosciences and Engineering, Journal Name: Mathematical Biosciences and Engineering Journal Issue: 8 Vol. 22; ISSN 1551-0018

Publisher:: AIMS PressCopyright Statement

Country of Publication:: United States

Language:: English

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Related Subjects

Gause model
Stochastic differential equations
invariant distribution
noise-induced extinction
stochastic population

The Stochastic Gause Predator-Prey model: Noise-induced extinctions and invariance

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