Stability trichotomy, path stability, and relative stability for positive nonlinear difference equations of higher order

DOI10.1080/10236199508808032zbMath0855.39005OpenAlexW1982094715MaRDI QIDQ4890073

Ulrich Krause

Publication date: 4 February 1997

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

Full work available at URL: https://doi.org/10.1080/10236199508808032

zbMATH Keywords

path stabilitystability trichotomypositive discrete dynamical systemspositive nonlinear difference equations

Mathematics Subject Classification ID

Related Items (9)

Global behavior of solutions of a periodically forced Sigmoid Beverton–Holt model ⋮ Positive nonlinear difference equations ⋮ Stability of non-autonomous population models with bounded and periodic enforcement ⋮ Boundedness and Stability for Higher Order Difference Equations^* ⋮ The dynamics of \(x_{n+1}= \frac {\alpha + \beta x_n}{A+Bx_n+Cx_{n-1}}\) facts and conjectures ⋮ A limit set trichotomy for positive nonautonomous discrete dynamical systems ⋮ Asymptotic behavior of a nonhomogeneous linear recurrence system ⋮ The asymptotic behavior of monotone difference equations of higher order ⋮ Stability of certain nonautonomous difference equations

Cites Work

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• Strong ergodicity for strictly increasing nonlinear operators
• A nonlinear extension of the Birkhoff-Jentzsch theorem
• Relative stability for ascending and positively homogeneous operators on Banach spaces
• On rational recursive sequences
• Asymptotic Properties for Inhomogeneous Iterations of Nonlinear Operators
• A limit set trichotomy for monotone nonlinear dynamical systems
• A limit set trichotomy for self-mappings of normal cones in banach spaces

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