Persistence and spatial patterns in a one-predator-two-prey Lotka- Volterra model with diffusion

DOI10.1007/BF01759645zbMath0758.92015OpenAlexW2061649030WikidataQ115610245 ScholiaQ115610245MaRDI QIDQ1200288

S. Singh

Publication date: 16 January 1993

Published in: Annali di Matematica Pura ed Applicata. Serie Quarta (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf01759645

zbMATH Keywords

Lotka-Volterra systemTuring instabilitybounded smooth domainone predatordiffusion induced instabilityhomogeneous von Neumann boundary conditionsthree species systemtime-invariant patternstime-periodic spatial patternstwo competing prey species

Mathematics Subject Classification ID

Stability in context of PDEs (35B35) Reaction-diffusion equations (35K57) Population dynamics (general) (92D25) Ecology (92D40) Bifurcations in context of PDEs (35B32)

Related Items (9)

Dynamics of a predator-prey system with three species ⋮ Spatial patterns in population conflicts ⋮ Uniform persistence in reaction-diffusion plankton models ⋮ Pattern formation in a predator-mediated coexistence model with prey-taxis ⋮ Diffusive predator-prey models with stage structure on prey and Beddington-DeAngelis functional responses ⋮ Permanence and the dynamics of biological systems ⋮ A diffusive one-prey and two-competing-predator system with a ratio-dependent functional response. I: Long time behavior and stability of equilibria ⋮ A diffusive one-prey and two-competing-predator system with a ratio-dependent functional response. II: Stationary pattern formation ⋮ Asymptotical behaviors of a general diffusive consumer-resource model with maturation delay

Cites Work

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• Persistence in models of three interacting predator-prey populations
• Stable spatio-temporal oscillations of diffusive Lotka-Volterra system with three or more species
• Persistence in models of predator-prey populations with diffusion
• Geometric theory of semilinear parabolic equations
• The diffusive Lotka-Volterra system with three species can have a stable non-constant equilibrium solution
• Topics in stability and bifurcation theory

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