n -dimensional Kolmogorov maps, carrying simplices, and bifurcations at the origin

DOI10.1080/10236198.2023.2265511OpenAlexW4387609211MaRDI QIDQ6197573

Publication date: 20 March 2024

Published in: Journal of Difference Equations and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/10236198.2023.2265511

zbMATH Keywords

Lyapunov function bifurcation attractivity carrying simplex discrete competitive model Kolmogorov map LPA map retrotone map

Mathematics Subject Classification ID

Attractors and repellers of smooth dynamical systems and their topological structure (37C70) Fixed points and periodic points of dynamical systems; fixed-point index theory; local dynamics (37C25) Dynamical aspects of attractors and their bifurcations (37G35)

Cites Work

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On heteroclinic cycles of competitive maps via carrying simplices
On the equivalent classification of three-dimensional competitive Leslie/Gower models via the boundary dynamics on the carrying simplex
Carrying simplices in discrete competitive systems and age-structured semelparous popula\-tions
Smoothness of the carrying simplex for discrete-time competitive dynamical systems: A characterization of neat embedding
Periodic competitive differential equations and the discrete dynamics of competitive maps
Discrete time models for two-species competition
Uniqueness and attractivity of the carrying simplex for discrete-time competitive dynamical systems
Linearization and invariant manifolds on the carrying simplex for competitive maps
Two-parameter bifurcations in LPA model
The Jacobian matrix and global univalence of mappings
Convex geometry of the carrying simplex for the May-Leonard map
Differentiability of the remainder term in Taylor's formula
Bifurcation analysis of the flour beetle population growth equations
On existence and uniqueness of the carrying simplex for competitive dynamical systems
Matrix Analysis
Systems of differential equations which are competitive or cooperative: III. Competing species
Cycle Chains and the LPA Model
Trivial dynamics in discrete-time systems: carrying simplex and translation arcs
TheC¹property of convex carrying simplices for three-dimensional competitive maps
Global stability in a nonlinear difference-delay equation model of flour beetle population growth
Exclusion and dominance in discrete population models via the carrying simplex
Geometry of carrying simplices of 3-species competitive Lotka–Volterra systems
On existence and uniqueness of a modified carrying simplex for discrete Kolmogorov systems
On the dynamics of multi-species Ricker models admitting a carrying simplex
On the global behaviour of the LPA model when c_PA = 0

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