Border collision and fold bifurcations in a family of one-dimensional discontinuous piecewise smooth maps: divergence and bounded dynamics

DOI10.1080/10236198.2015.1046855zbMath1360.37127OpenAlexW1849491987MaRDI QIDQ3448513

Laura Gardini, Roya Makrooni, Farhad Khellat

Publication date: 26 October 2015

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

Full work available at URL: https://doi.org/10.1080/10236198.2015.1046855

zbMATH Keywords

piecewise smooth mapsunbounded chaotic setscodimension-two bifurcation pointsbifurcations of repelling cycleschaotic repellors

Mathematics Subject Classification ID

Bifurcations of limit cycles and periodic orbits in dynamical systems (37G15) Dynamical systems involving maps of the interval (37E05)

Related Items (5)

Bifurcation Analysis of a Piecewise Smooth Map with Two Asymptotes ⋮ 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 ⋮ Poverty trap, boom and bust periods and growth. A nonlinear model for non-developed and developing countries ⋮ Bifurcation Structures in a Family of 1D Discontinuous Linear-Hyperbolic Invertible Maps

Cites Work

• Border-collision bifurcations in a generalized piecewise linear-power map
• Snap-back repellers imply chaos in \(\mathbb{R}^n\)
• Bifurcations of dynamical systems with sliding: derivation of normal-form mappings
• Piecewise-smooth dynamical systems. Theory and applications
• On redefining a snap-back repeller
• Influence of a square-root singularity on the behaviour of piecewise smooth maps
• Grazing, skipping and sliding: Analysis of the non-smooth dynamics of the DC/DC buck converter
• Homoclinic bifurcations in n-dimensional endomorphisms, due to expanding periodic points
• Feedback control of limit cycles: a switching control strategy based on nonsmooth bifurcation theory
• NONSMOOTH AND SMOOTH BIFURCATIONS IN A DISCONTINUOUS PIECEWISE MAP
• Corner collision implies border-collision bifurcation

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