Non-autonomous periodic systems with Allee effects

DOI10.1080/10236190902794951zbMath1204.39016OpenAlexW2106408717MaRDI QIDQ3163031

Rafael Luís, Henrique M. Oliveira, Saber N. Elaydi

Publication date: 22 October 2010

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

Full work available at URL: https://digitalcommons.trinity.edu/math_faculty/13

zbMATH Keywords

stabilityfixed pointperiodic systemsbifurcationdifference equationspopulation dynamicscarrying capacitythreshold pointcomposition mapnon-autonomous periodic dynamical systemsunimodal Allee maps

Mathematics Subject Classification ID

Population dynamics (general) (92D25) Discrete version of topics in analysis (39A12) Fixed points and periodic points of dynamical systems; fixed-point index theory; local dynamics (37C25) Periodic solutions of difference equations (39A23) Stability theory for difference equations (39A30)

Related Items (26)

Towards a Theory of Periodic Difference Equations and Its Application to Population Dynamics ⋮ Extinction and the Allee effect in an age structured Ricker population model with inter-stage interaction ⋮ Multi-transitivity in non-autonomous discrete systems ⋮ On almost continuous functions and peculiar points ⋮ Limits for density dependent time inhomogeneous Markov processes ⋮ Random Dynamical Systems Generated by Two Allee Maps ⋮ ON FUNCTIONS ATTRACTING POSITIVE ENTROPY ⋮ Mean Li-Yorke chaos and mean sensitivity in non-autonomous discrete systems ⋮ STABLE, ALMOST STABLE AND ODD POINTS OF DYNAMICAL SYSTEMS ⋮ Periodic unimodal Allee maps, the semigroup property and the \(\lambda\)-Ricker map with Allee effect ⋮ Difference population equation with variable Allee effect and periodic carrying capacity ⋮ On the local aspects of distributional chaos ⋮ Hierarchical competition models with the Allee effect III: multispecies ⋮ Global behavior of solutions of a periodically forced Sigmoid Beverton–Holt model ⋮ Discrete-time host–parasitoid models with pest control ⋮ General Allee effect in two-species population biology ⋮ Difference equations with the Allee effect and the periodic Sigmoid Beverton–Holt equation revisited ⋮ Pushed beyond the brink: Allee effects, environmental stochasticity, and extinction ⋮ Hierarchical competition models with the Allee effect II: the case of immigration ⋮ Hierarchical competition models with Allee effects ⋮ Sensitivity and property \(P\) in non-autonomous systems ⋮ Multiple attractors in a Leslie–Gower competition system with Allee effects ⋮ Furstenberg family and multi-sensitivity in non-autonomous systems ⋮ LOCAL BIFURCATION IN ONE-DIMENSIONAL NONAUTONOMOUS PERIODIC DIFFERENCE EQUATIONS ⋮ A model of band-pass phenotypic resistance in a modified Beverton-Holt framework ⋮ Furstenberg family and multi-transitivity in non-autonomous systems

Cites Work

• Global stability of periodic orbits of non-autonomous difference equations and population biology
• An extension of Sharkovsky's theorem to periodic difference equations
• On the periodic logistic equation
• Oscillations in age-structured population models with an Allee effect
• Multiple attractors and resonance in periodically forced population models
• Allee effects, extinctions, and chaotic transients in simple population models
• Multiple Attractors in Juvenile-adult Single Species Models
• Population models with Allee effect: a new model
• An extended discrete Ricker population model with Allee effects
• Allee effects in a discrete-time SIS epidemic model with infected newborns
• Pitchfork bifurcation for non-autonomous interval maps
• On the periodically perturbed logistic equation
• An economical model with Allee effect
• Allee effects in a discrete-time host-parasitoid model
• Population extinction in discrete-time stochastic population models with an Allee effect
• Nonautonomous Beverton-Holt equations and the Cushing-Henson conjectures
• On the structure of attractors for discrete, periodically forced systems with applications to population models

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