Uniqueness and attractivity of the carrying simplex for discrete-time competitive dynamical systems
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Publication:1867239
DOI10.1016/S0022-0396(02)00025-6zbMath1026.37016OpenAlexW1974884074MaRDI QIDQ1867239
Publication date: 2 April 2003
Published in: Journal of Differential Equations (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/s0022-0396(02)00025-6
Stability of topological dynamical systems (37B25) Attractors and repellers of smooth dynamical systems and their topological structure (37C70)
Related Items (36)
Saddle-point behavior for monotone semiflows and reaction-diffusion models ⋮ Dynamics of the periodic type-\(K\) competitive Kolmogorov systems ⋮ Convex geometry of the carrying simplex for the May-Leonard map ⋮ On Lotka--Volterra Equations with Identical Minimal Intrinsic Growth Rate ⋮ Trivial dynamics in discrete-time systems: carrying simplex and translation arcs ⋮ On the classification of generalized competitive Atkinson-Allen models via the dynamics on the boundary of the carrying simplex ⋮ Čech cohomology of attractors of discrete dynamical systems ⋮ Three limit cycles for 3D Ricker competitive system ⋮ On global dynamics of type-K competitive Kolmogorov differential systems ⋮ The property of convex carrying simplices for competitive maps ⋮ Necessary and sufficient conditions for the existence of equilibrium in abstract non-autonomous functional differential equations ⋮ Global attraction and repulsion of a heteroclinic limit cycle in three dimensional Kolmogorov maps ⋮ n -dimensional Kolmogorov maps, carrying simplices, and bifurcations at the origin ⋮ On existence and uniqueness of the carrying simplex for competitive dynamical systems ⋮ Unnamed Item ⋮ On existence and uniqueness of a carrying simplex in Kolmogorov differential systems ⋮ Chaotic attractors in the four-dimensional Leslie-Gower competition model ⋮ Carrying simplices in nonautonomous and random competitive Kolmogorov systems ⋮ Chaotic attractors in Atkinson–Allen model of four competing species ⋮ On the equivalent classification of three-dimensional competitive Leslie/Gower models via the boundary dynamics on the carrying simplex ⋮ Linearization and invariant manifolds on the carrying simplex for competitive maps ⋮ TheC1property of convex carrying simplices for three-dimensional competitive maps ⋮ Manifolds of balance in planar ecological systems ⋮ Carrying simplex in the Lotka-Volterra competition model with seasonal succession with applications ⋮ On the dynamics of multi-species Ricker models admitting a carrying simplex ⋮ Invariant manifolds of competitive selection-recombination dynamics ⋮ On the equivalent classification of three-dimensional competitive Atkinson/Allen models relative to the boundary fixed points ⋮ Smoothness of the carrying simplex for discrete-time competitive dynamical systems: A characterization of neat embedding ⋮ On a boom and bust year class cycle ⋮ Monotone maps: a review ⋮ Permanence and universal classification of discrete-time competitive systems via the carrying simplex ⋮ On existence and uniqueness of a modified carrying simplex for discrete Kolmogorov systems ⋮ Geometric method for global stability of discrete population models ⋮ Competitive systems with migration and the Poincaré-Bendixson theorem for a 4-dimensional case ⋮ A 3D competitive Lotka-Volterra system with three limit cycles: a falsification of a conjecture by Hofbauer and So ⋮ On heteroclinic cycles of competitive maps via carrying simplices
Cites Work
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- Periodic competitive differential equations and the discrete dynamics of competitive maps
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- The long-run behavior of periodic competitive Kolmogorov systems
- Boundedness of Prime Periods of Stable Cycles and Convergence to Fixed Points in Discrete Monotone Dynamical Systems
- Systems of differential equations which are competitive or cooperative: III. Competing species
- Chain transitive sets for smooth strongly monotone dynamical systems
- An exclusion principle for periodic competitive systems in three dimensions
- On Li-Yorke pairs
- The general properties of dicrete-time competitive dynamical systems
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