Solving Volterra-Lotka systems with diffusion by monotone iteration

DOI10.1007/BF00168177zbMath0735.35060WikidataQ113910135 ScholiaQ113910135MaRDI QIDQ1174294

R. L. Voller

Publication date: 25 June 1992

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

zbMATH Keywords

Dirichlet problemconvex domainpredator-prey systemsubsolutionsmonotone iteration methodstationary Volterra-Lotka system

Mathematics Subject Classification ID

Nonlinear boundary value problems for linear elliptic equations (35J65) Population dynamics (general) (92D25)

Uses Software

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Cites Work

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• On the monotone convergence of Newton's method
• Finite difference approximations to the Dirichlet problem for elliptic systems
• Convergence to the equilibrium state in the Volterra-Lotka diffusion equations
• Limiting behaviour for a prey-predator model with diffusion and crowding effects
• On Positive Solutions of Some Pairs of Differential Equations
• Bifurcation of steady-state solutions in predator-prey and competition systems
• On the dirichlet problem for elliptic systems
• A general monotone scheme for elliptic systems with applications to ecological models
• Newton-like methods with monotone convergence for solving nonlinear operator equations
• On the existence and uniqueness of positive steady states in the volterra-lotka ecological models with diffusion
• Stationary solutions of reaction-diffusion equations
• Ein neues Verfahren zur Einschließung der Lösungen von Operatorgleichungen

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