Multi-dimensional Lotka-Volterra systems for carcinogenesis mutations

DOI10.1002/mma.1137zbMath1181.35129OpenAlexW2116034545MaRDI QIDQ3647155

Urszula Fory's

Publication date: 30 November 2009

Published in: Mathematical Methods in the Applied Sciences (Search for Journal in Brave)

Full work available at URL: https://rcin.org.pl/dlibra/docmetadata?showContent=true&id=32223

zbMATH Keywords

invariant setdissipativityLyapunov functionalfood chainlocal and global stabilitymalignant cellsbenign cells

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Reaction-diffusion equations (35K57) PDEs in connection with biology, chemistry and other natural sciences (35Q92) Medical applications (general) (92C50) Population dynamics (general) (92D25) Qualitative investigation and simulation of ordinary differential equation models (34C60) Global stability of solutions to ordinary differential equations (34D23) Asymptotic properties of solutions to ordinary differential equations (34D05) Semilinear parabolic equations (35K58) Initial-boundary value problems for second-order parabolic systems (35K51)

Related Items (7)

Qualitative and computational analysis of a mathematical model for tumor-immune interactions ⋮ Analysis of the Hopf bifurcation for the family of angiogenesis models. II: The case of two nonzero unequal delays ⋮ Chaos in a tumor growth model with delayed responses of the immune system ⋮ About a generalized model of lymphoma ⋮ Stability problem for the age-dependent predator-prey model ⋮ What can be learned from a chaotic cancer model? ⋮ Two-stage model of carcinogenic mutations with the influence of delays

Cites Work

• Persistence in food webs - I. Lotka-Volterra food chains
• Geometric theory of semilinear parabolic equations
• Individual-based approaches to birth and death in avascular tumors
• A survey of models for tumor-immune system dynamics
• THREE TYPES OF SIMPLE DDE'S DESCRIBING TUMOR GROWTH
• Stability Analysis and Comparison of the Models for Carcinogenesis Mutations in the Case of Two Stages of Mutations
• MODELLING OF EARLY LUNG CANCER PROGRESSION: INFLUENCE OF GROWTH FACTOR PRODUCTION AND COOPERATION BETWEEN PARTIALLY TRANSFORMED CELLS
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