Local stability implies global stability for the planar Ricker competition model

DOI10.3934/dcdsb.2014.19.323zbMath1282.39016OpenAlexW2117405499MaRDI QIDQ2438853

Rafael Luís, Saber N. Elaydi, Eduardo Cabral Balreira

Publication date: 7 March 2014

Published in: Discrete and Continuous Dynamical Systems. Series B (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3934/dcdsb.2014.19.323

zbMATH Keywords

cuspglobal stabilitylocal stabilitycritical curvescompetition modelfoldcompact invariant setprincipal preimage function

Mathematics Subject Classification ID

Critical points and critical submanifolds in differential topology (57R70) Stability theory for difference equations (39A30) Applications of difference equations (39A60)

Related Items (24)

Attraction in nonmonotone planar systems and real-life models ⋮ Local stability in 3D discrete dynamical systems: application to a Ricker competition model ⋮ Bifurcation in the almost periodic \(2\)D Ricker map ⋮ Dynamics of the discrete-time Rosenzweig-MacArthur predator-prey system in the closed positively invariant set ⋮ On a Stochastic Ricker Competition Model ⋮ An augmented phase plane approach for discrete planar maps: introducing next-iterate operators ⋮ Geometry and global stability of 2D periodic monotone maps ⋮ A global picture for the planar Ricker map: convergence to fixed points and identification of the stable/unstable manifolds ⋮ Global stability of Beddington model ⋮ A note on a parameter bound for global stability in the 2D Coupled Ricker equation ⋮ Global dynamics of triangular maps ⋮ Qualitative structures of a degenerate fixed point of a Ricker competition model ⋮ Discrete evolutionary population models: a new approach ⋮ Stability and invariant manifolds of a generalized Beddington host-parasitoid model ⋮ Competitive exclusion and coexistence in ann-species Ricker model ⋮ Global asymptotical stability of the coexistence fixed point of a Ricker-type competitive model ⋮ Global stability in the 2D Ricker equation revisited ⋮ Complexity and chaos control in a discrete-time prey-predator model ⋮ On the dynamics of multi-species Ricker models admitting a carrying simplex ⋮ Dynamics of the discrete Seno population model: combined effects of harvest timing and intensity on population stability ⋮ Complexity and chaos control in a discrete-time Lotka–Volterra predator–prey system ⋮ A sufficient condition for stability using slopes of isoclines in planar mappings ⋮ Global asymptotical stability of the positive equilibrium of a logistic competitive model ⋮ The effects of evolution on the stability of competing species

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