Nested Closed Invariant Curves in Piecewise Smooth Maps

DOI10.1142/S0218127419300179zbMath1423.37043OpenAlexW2958300721WikidataQ127485011 ScholiaQ127485011MaRDI QIDQ5229103

Zhanybai T. Zhusubaliyev, Viktor Avrutin

Publication date: 14 August 2019

Published in: International Journal of Bifurcation and Chaos (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/s0218127419300179

zbMATH Keywords

multistabilitypiecewise smooth systemsclosed invariant curvestwo-dimensional piecewise-linear border collision normal form

Mathematics Subject Classification ID

Attractors and repellers of smooth dynamical systems and their topological structure (37C70) Normal forms for dynamical systems (37G05) Dynamical systems involving homeomorphisms and diffeomorphisms of planes and surfaces (37E30) Invariant manifold theory for dynamical systems (37D10)

Related Items (2)

Analysis of atypical orbits in one-dimensional piecewise-linear discontinuous maps ⋮ Border collision and heteroclinic bifurcations in a 2D piecewise smooth map

Cites Work

• Unnamed Item
• Occurrence of multiple attractor bifurcations in the two-dimensional piecewise linear normal form map
• Control of multistability
• Equilibrium-torus bifurcation in nonsmooth systems
• Border-collision bifurcations including ``period two to period three for piecewise smooth systems
• Border-collision bifurcations on a two-dimensional torus
• Controlling coexisting attractors of an impacting system via linear augmentation
• Co-existing attractors of impact oscillator
• Multistability and hidden attractors in a multilevel DC/DC converter
• The structure of mode-locking regions of piecewise-linear continuous maps: I. Nearby mode-locking regions and shrinking points
• TORUS BIFURCATIONS IN MULTILEVEL CONVERTER SYSTEMS
• Sequences of Periodic Solutions and Infinitely Many Coexisting Attractors in the Border-Collision Normal Form
• Border collision route to quasiperiodicity: Numerical investigation and experimental confirmation
• Shrinking point bifurcations of resonance tongues for piecewise-smooth, continuous maps
• Piecewise linear models for the quasiperiodic transition to chaos
• The structure of mode-locking regions of piecewise-linear continuous maps: II. Skew sawtooth maps
• Extreme multistability: Attractor manipulation and robustness
• Multistability and arithmetically period-adding bifurcations in piecewise smooth dynamical systems
• Elements of applied bifurcation theory

This page was built for publication: Nested Closed Invariant Curves in Piecewise Smooth Maps