Robust unbounded chaotic attractors in 1D discontinuous maps

DOI10.1016/j.chaos.2015.06.012zbMath1353.37083OpenAlexW2291831253MaRDI QIDQ502763

Laura Gardini, Neda Abbasi, Mehdi Pourbarat, Roya Makrooni

Publication date: 11 January 2017

Published in: Chaos, Solitons and Fractals (Search for Journal in Brave)

Full work available at URL: http://www.econ.uniurb.it/RePEc/urb/wpaper/WP_15_01.pdf

zbMATH Keywords

border collision bifurcationspiecewise smooth systemsfull shift mapsrobust full measure chaotic attractorsunbounded chaotic attractors

Mathematics Subject Classification ID

Stability of topological dynamical systems (37B25) Simulation of dynamical systems (37M05) Dynamical systems involving maps of the interval (37E05)

Related Items (6)

Bifurcation Analysis of a Piecewise Smooth Map with Two Asymptotes ⋮ Two regularizations of the grazing-sliding bifurcation giving non equivalent dynamics ⋮ Border collision and fold bifurcations in a family of one-dimensional discontinuous piecewise smooth maps: unbounded chaotic sets ⋮ Cascades of alternating smooth bifurcations and border collision bifurcations with singularity in a family of discontinuous linear-power maps ⋮ Chaos in one-dimensional piecewise smooth dynamical systems ⋮ Necessary and sufficient conditions of full chaos for expanding Baker-like maps and their use in non-expanding Lorenz maps

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Linear chaos
• Border-collision bifurcations in a generalized piecewise linear-power map
• Chaotic behaviour of the general symbolic dynamics
• Cyclicity of chaotic attractors in one-dimensional discontinuous maps
• Piecewise-smooth dynamical systems. Theory and applications
• APPLICATIONS OF SYMBOLIC DYNAMICS ON AN INFINITE ALPHABET
• BORDER-COLLISION BIFURCATIONS IN 1D PIECEWISE-LINEAR MAPS AND LEONOV'S APPROACH
• BORDER COLLISION BIFURCATIONS IN 1D PWL MAP WITH ONE DISCONTINUITY AND NEGATIVE JUMP: USE OF THE FIRST RETURN MAP
• On multi-parametric bifurcations in a scalar piecewise-linear map
• On Devaney's Definition of Chaos
• On Intervals, Transitivity = Choas
• CLARIFYING CHAOS: EXAMPLES AND COUNTEREXAMPLES
• NONSMOOTH AND SMOOTH BIFURCATIONS IN A DISCONTINUOUS PIECEWISE MAP
• Codimension-2 Border Collision, Bifurcations in One-Dimensional, Discontinuous Piecewise Smooth Maps
• Robust Chaos
• UNBOUNDED SETS OF ATTRACTION

This page was built for publication: Robust unbounded chaotic attractors in 1D discontinuous maps