A classification theorem for three dimensional competitive systems
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Publication:1099317
DOI10.1016/0022-0396(87)90154-9zbMath0638.34022OpenAlexW2016297725MaRDI QIDQ1099317
Paul Waltman, Hal Leslie Smith
Publication date: 1987
Published in: Journal of Differential Equations (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/0022-0396(87)90154-9
phase portraitsglobal dynamicsbasins of attractionfirst order differential equationKolmogorov-type competitive system
Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Population dynamics (general) (92D25)
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On Lotka--Volterra Equations with Identical Minimal Intrinsic Growth Rate ⋮ Systems of differential equations that are competitive or cooperative. VI: A localCrClosing Lemma for 3-dimensional systems ⋮ On the validity of Zeeman's classification for three dimensional competitive differential equations with linearly determined nullclines ⋮ Systems of differential equations that are competitive or cooperative. V: Convergence in 3-dimensional systems ⋮ On the complete classification of nullcline stable competitive three-dimensional Gompertz models
Cites Work
- Persistence in a model of three competitive populations
- On the differential equations of species in competition
- Periodic orbits of competitive and cooperative systems
- The dynamical systems approach to differential equations
- Uniformly Persistent Systems
- Systems of Differential Equations that are Competitive or Cooperative II: Convergence Almost Everywhere
- Systems of Ordinary Differential Equations Which Generate an Order Preserving Flow. A Survey of Results
- On $\omega $-Limits for Competition Between Three Species
- Systems of Differential Equations Which Are Competitive or Cooperative: I. Limit Sets
- Persistence in dynamical systems
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