Bifurcation and invariant manifolds of the logistic competition model

DOI10.1080/10236198.2010.504377zbMath1244.39012OpenAlexW1987603450MaRDI QIDQ3103833

Rafael Luís, Małgorzata Guzowska, Saber N. Elaydi

Publication date: 12 December 2011

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

Full work available at URL: https://digitalcommons.trinity.edu/cgi/viewcontent.cgi?article=1000&context=math_faculty

zbMATH Keywords

stabilityperiodic solutionschaosbifurcationcompetition modelrational difference equationscentre manifoldsunstable and stable manifolds

Mathematics Subject Classification ID

Multiplicative and other generalized difference equations (39A20) Stability theory for difference equations (39A30) Bifurcation theory for difference equations (39A28) Chaotic behavior of solutions of difference equations (39A33)

Related Items (13)

Linear stability conditions for a first order \(n\)-dimensional mapping ⋮ Attractors of randomly forced logistic model with delay: stochastic sensitivity and noise-induced transitions ⋮ Local stability in 3D discrete dynamical systems: application to a Ricker competition model ⋮ Analysis of noise-induced transitions in a generalized logistic model with delay near Neimark–Sacker bifurcation ⋮ Local stability implies global stability for the planar Ricker competition model ⋮ Global dynamics of triangular maps ⋮ General Allee effect in two-species population biology ⋮ Stability and invariant manifolds of a generalized Beddington host-parasitoid model ⋮ Complexity and chaos control in a discrete-time Lotka–Volterra predator–prey system ⋮ A discrete-time model for consumer-resource interaction with stability, bifurcation and chaos control ⋮ 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 stability of a degenerate fixed point for Guzowska–Luís–Elaydi model

Cites Work

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• Global dynamics in macroeconomics: An overlapping generations example
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• The stable, center-stable, center, center-unstable, unstable manifolds
• The center manifold theorem for a discrete system
• THE PROPERTIES OF A STOCHASTIC MODEL FOR TWO COMPETING SPECIES
• The parameterization method for invariant manifolds I: Manifolds associated to non-resonant subspaces
• Some Discrete Competition Models and the Competitive Exclusion Principle^†
• Introduction to Applied Nonlinear Dynamical Systems and Chaos

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