Perturbations of stable and chaotic difference equations

DOI10.1016/0022-247X(79)90259-2zbMath0425.58015MaRDI QIDQ1135559

Frederick R. Marotto

Publication date: 1979

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

zbMATH Keywords

snap-back repellerchaoscompetition modelsLeslie modelHenon mappingtransversal homoclinic orbitchaotic behavior in discrete dynamical systemsstability of chaosstable fixed or periodic point

Mathematics Subject Classification ID

Related Items (21)

Transition to topological chaos for circle maps ⋮ Stability and attractivity in discrete dynamical systems ⋮ The topological conjugacy problem for generalized Hénon mappings: some negative results ⋮ Some dynamics of second order unimodal difference schemes ⋮ Chaotic behavior in the Henon mapping ⋮ HETEROCLINICAL REPELLERS IMPLY CHAOS ⋮ Period doubling and quadrupling for some second-order difference schemes ⋮ Li–Yorke Chaos in Perturbed Rational Difference Equations ⋮ Chaos resulting from nonlinear relations between different variables ⋮ Stability of symbolic embeddings for difference equations and their multidimensional perturbations ⋮ From chaos to global convergence ⋮ Structure stability of maps with snap-back repellers in Banach spaces ⋮ Chaotic dynamics in a two-dimensional overlapping generations model. ⋮ Transversal homoclinic orbits in a transiently chaotic neural network ⋮ Stochastic properties in Devaney's chaos ⋮ Linear Generalized Synchronization of Spatial Chaotic Systems ⋮ A simple proof for persistence of snap-back repellers ⋮ ON THE MATHEMATICAL CLARIFICATION OF THE SNAP-BACK-REPELLER IN HIGH-DIMENSIONAL SYSTEMS AND CHAOS IN A DISCRETE NEURAL NETWORK MODEL ⋮ Homoclinic shadowing ⋮ Chaotic dynamics in quasi-static systems: Theory and applications ⋮ Chaos, complex transients and noise: illustration with a Kaldor model.

Cites Work

• A two-dimensional mapping with a strange attractor
• Discrete time models for two-species competition
• The dynamics of density dependent population models
• Snap-back repellers imply chaos in \(\mathbb{R}^n\)
• On the nature of turbulence
• Period Three Implies Chaos
• Differentiable dynamical systems
• Invariant manifolds
• Unnamed Item

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