On parabolic systems of the volterra predator–prey type

DOI10.1016/0362-546X(83)90087-1zbMath0515.92021OpenAlexW1984104696WikidataQ115599075 ScholiaQ115599075MaRDI QIDQ3663062

Wolfgang Walter, Raymond M. Redheffer

Publication date: 1983

Published in: Nonlinear Analysis: Theory, Methods & Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0362-546x(83)90087-1

zbMATH Keywords

omega-limit setinteracting populationsnonconstant periodic solutiongraph theoretic methodsasymptotically stable stationary pointsreaction- diffusion modelsVolterra prey-predator systems

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Nonlinear parabolic equations (35K55) Population dynamics (general) (92D25)

Related Items (9)

Compactness results for time-dependent parabolic systems ⋮ On the dirichlet problem for elliptic systems ⋮ A qualitative analysis of \(\dot x=Ax+b\) ⋮ Shape-invariant bounds for reaction-diffusion systems with unequal diffusion coefficients ⋮ Orbital compactness and asymptotic behaviour of nonlinear parabolic systems with functionals ⋮ Eigenvalues, stability, and color tests ⋮ Stability of mass action reaction-diffusion systems. ⋮ Stability of mass action reaction-diffusion systems ⋮ Volterra Multipliers I

Cites Work

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• Diffusion in Fisher's population model
• Invariant sets and existence theorems for semilinear parabolic and elliptic systems
• The Volterra model for three species predator-prey systems: Boundedness and stability
• Stability theory for ordinary differential equations
• A Class of Matrices Connected with Volterra Prey-Predator Equations

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