Coexistence of the bandcount-adding and bandcount-increment scenarios
type: Item
instance of: scholarly article
title: Coexistence of the bandcount-adding and bandcount-increment scenarios
zbMATH Open document ID: 1231.37023
DOI: 10.1155/2011/681565
author: Viktor Avrutin
author: Michael Schanz
author: Björn Schenke
published in: Discrete Dynamics in Nature and Society
publication date: 2012-01-23T00:00:00Z
review text: Summary: We investigate the structure of the chaotic domain of a specific one-dimensional piecewise linear map with one discontinuity. In this system, the region of ``robust'' chaos is embedded between two periodic domains. One of them is organized by the period-adding scenario and the other by the period-increment scenario with coexisting attractors. In the chaotic domain, the influence of both adjacent periodic domains leads to the coexistence of the recently discovered bandcount-adding and bandcount-increment scenarios. In this work, we focus on the explanation of the overall structure of the chaotic domain and a description of the bandcount-adding and bandcount-increment scenarios.
Mathematics Subject Classification ID: 37E05
Mathematics Subject Classification ID: 37D45
Mathematics Subject Classification ID: 37B10
Mathematics Subject Classification ID: 37N99
Mathematics Subject Classification ID: 37G15
zbMATH DE Number: 5999651
Wikidata QID: Q57627266
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2011/681565
OpenAlex ID: W1986811379
cites work: Q4435200
cites work: Piecewise-smooth dynamical systems. Theory and applications
cites work: Q3654873
cites work: The simplified Fermi accelerator in classical and quantum mechanics
cites work: On the Origin of the Cosmic Radiation
cites work: Mappings of grazing-impact oscillators
cites work: BORDER-COLLISION BIFURCATIONS IN ONE-DIMENSIONAL DISCONTINUOUS MAPS
cites work: Border-collision bifurcations including ``period two to period three'' for piecewise smooth systems
cites work: BORDER-COLLISION BIFURCATIONS FOR PIECEWISE SMOOTH ONE-DIMENSIONAL MAPS
cites work: On period-adding sequences of attracting cycles in piecewise linear maps
cites work: The bandcount increment scenario. I. Basic structures
cites work: The bandcount increment scenario. II. Interior structures
cites work: The bandcount increment scenario. III. Deformed structures
cites work: On the fully developed bandcount adding scenario
cites work: Multi-parametric bifurcations in a piecewise–linear discontinuous map
cites work: Robust Chaos
cites work: Q4126160
cites work: Q4146638
cites work: Q3885588
cites work: Crises, sudden changes in chaotic attractors, and transient chaos
cites work: Universality and scaling in chaotic attractor-to-chaotic attractor transitions.
cites work: Chaos in driven Alfvén systems: boundary and interior crises
cites work: Attractor merging crisis in chaotic business cycles
cites work: Complex economic dynamics: Chaotic saddle, crisis and intermittency
cites work: Chaos crisis in coupled Duffing's systems with initial phase difference
cites work: Q4040292
cites work: Q4871304
cites work: On multi-parametric bifurcations in a scalar piecewise-linear map
cites work: DEGENERATE BIFURCATIONS AND BORDER COLLISIONS IN PIECEWISE SMOOTH 1D AND 2D MAPS
cites work: BORDER-COLLISION BIFURCATIONS IN 1D PIECEWISE-LINEAR MAPS AND LEONOV'S APPROACH
cites work: On detection of multi-band chaotic attractors
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description: scientific article; zbMATH DE number 5999651