Kolmogorov vector fields with robustly permanent subsystems

DOI10.1006/jmaa.2001.7776zbMath1017.34052OpenAlexW2021815153MaRDI QIDQ5961168

Sebastian J. Schreiber, Janusz Mierczyński

Publication date: 16 October 2002

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://semanticscholar.org/paper/ed42f7041e91a0ddca73919cfe8baa364f16e9f8

zbMATH Keywords

invariant setsattractorpermanenceKolmogorov equationsrepellerMorse decompositionergodic probability measureLotka-Volterra modelsLyaponov exponentsrobust permanence

Mathematics Subject Classification ID

Population dynamics (general) (92D25) Asymptotic properties of solutions to ordinary differential equations (34D05) Attractors of solutions to ordinary differential equations (34D45)

Related Items (14)

Uniform persistence for nonautonomous and random parabolic Kolmogorov systems ⋮ On global dynamics of type-K competitive Kolmogorov differential systems ⋮ The property of convex carrying simplices for competitive maps ⋮ Robust Permanence for Ecological Maps ⋮ On existence and uniqueness of a carrying simplex in Kolmogorov differential systems ⋮ Asymptotic behaviour and bifurcation in competitive Lotka-Volterra systems ⋮ Global stability of interior and boundary fixed points for Lotka-Volterra systems ⋮ Robust permanence for interacting structured populations ⋮ Partial persistence and extinction in \(N\)-dimensional competitive systems ⋮ On permanence of all subsystems of competitive Lotka-Volterra systems with delays ⋮ Average growth and total permanence in a competitive Lotka-Volterra System ⋮ Smoothness of the carrying simplex for discrete-time competitive dynamical systems: A characterization of neat embedding ⋮ Lower estimates of top Lyapunov exponent for cooperative random systems of linear ODEs ⋮ Permanence via invasion graphs: incorporating community assembly into modern coexistence theory

Cites Work

• Unnamed Item
• An index theorem for dissipative semiflows
• The \(C^ 1\) property of carrying simplices for a class of competitive systems of ODEs
• Criteria for \(C^r\) robust permanence
• Ergodic Properties of Linear Dynamical Systems
• Systems of differential equations which are competitive or cooperative: III. Competing species
• Abstract ω-Limit Sets, Chain Recurrent Sets, and Basic Sets for Flows
• On smoothness of carrying simplices
• Successional stability of vector fields in dimension three
• Evolutionary Games and Population Dynamics
• Chain transitivity, attractivity, and strong repellors for semidynamical systems

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