Geometric criteria for the nonexistence of cycles in Gause-type predator-prey systems

DOI10.1090/S0002-9939-05-08026-3zbMath1077.34056OpenAlexW1607344824WikidataQ115545941 ScholiaQ115545941MaRDI QIDQ5313344

Yaping Liu

Publication date: 29 August 2005

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0002-9939-05-08026-3

Mathematics Subject Classification ID

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Population dynamics (general) (92D25) Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert's 16th problem and ramifications) for ordinary differential equations (34C07) Global stability of solutions to ordinary differential equations (34D23)

Related Items

Effects of the self- and cross-diffusion on positive steady states for a generalized predator-prey system, Geometric criteria for the non-existence of cycles in predator-prey systems with group defense, A qualitative study on general Gause-type predator-prey models with constant diffusion rates, A predator-prey system with Holling-type functional response, Multiple stability and uniqueness of the limit cycle in a Gause-type predator-prey model considering the Allee effect on prey, The hydra effect in predator-prey models, Spatiotemporal complexity in a predator-prey model with weak Allee effects, A qualitative study on general Gause-type predator-prey models with non-monotonic functional response, Some uniqueness and multiplicity results for a predator-prey dynamics with a nonlinear growth rate

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