A stochastic model for predator-prey systems: basic properties, stability and computer simulation

DOI10.1007/BF00164048zbMath0737.92018WikidataQ52462366 ScholiaQ52462366MaRDI QIDQ1814080

Mario Abundo

Publication date: 25 June 1992

Published in: Journal of Mathematical Biology (Search for Journal in Brave)

zbMATH Keywords

momentssimulationextinction probabilityIto stochastic differential equationsdeterministic equilibriumevolution of a Lotka-Volterra prey-predator systeminfinitesimal covariance structuremartingale considerationstwo-dimensional continuous time Markov chain

Mathematics Subject Classification ID

Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) Population dynamics (general) (92D25) Applications of stochastic analysis (to PDEs, etc.) (60H30) Ecology (92D40)

Related Items (7)

On simulating strongly interacting, stochastic population models. II: Multiple compartments ⋮ Dynamic behavior of a predator-prey system of combined harvesting with interval-valued rate parameters ⋮ Unnamed Item ⋮ On simulating strongly-interacting, stochastic population models. ⋮ Effect of toxic substance on delayed competitive allelopathic phytoplankton system with varying parameters through stability and bifurcation analysis ⋮ Asymptotic dynamics of a deterministic and stochastic predator–prey model with disease in the prey species ⋮ New approach for stability and bifurcation analysis on predator-prey harvesting model for interval biological parameters with time delays

Cites Work

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• A diffusion model for population growth in random environment
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• Persistence of Dynamical Systems under Random Perturbations
• On Lotka–Volterra predator prey models
• The Lindeberg-Levy Theorem for Martingales
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