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Simultaneous border-collision and period-doubling bifurcations
We unfold the codimension-two simultaneous occurrence of a border-collision bifurcation and a period-doubling bifurcation for a general piecewise-smooth, continuous map. We find that with sufficient nondegeneracy conditions, a locus of period-doubling bifurcations emanates nontangentially from a loc...
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| Published in: | Chaos (Woodbury, N.Y.) N.Y.), 2009-09, Vol.19 (3), p.033146-033146-11 |
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| Main Authors: | , |
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| Language: | English |
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| cited_by | cdi_FETCH-LOGICAL-c509t-f3b90a46ab7698f42201544e6b01c0694e5cbc82e79064dbac0e04baaff048ad3 |
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| cites | cdi_FETCH-LOGICAL-c509t-f3b90a46ab7698f42201544e6b01c0694e5cbc82e79064dbac0e04baaff048ad3 |
| container_end_page | 033146-11 |
| container_issue | 3 |
| container_start_page | 033146 |
| container_title | Chaos (Woodbury, N.Y.) |
| container_volume | 19 |
| creator | Simpson, D. J. W. Meiss, J. D. |
| description | We unfold the codimension-two simultaneous occurrence of a border-collision bifurcation and a period-doubling bifurcation for a general piecewise-smooth, continuous map. We find that with sufficient nondegeneracy conditions, a locus of period-doubling bifurcations emanates nontangentially from a locus of border-collision bifurcations. The corresponding period-doubled solution undergoes a border-collision bifurcation along a curve emanating from the codimension-two point and tangent to the period-doubling locus here. In the case that the map is one-dimensional local dynamics is completely classified; in particular, we give conditions that ensure chaos. |
| doi_str_mv | 10.1063/1.3227645 |
| format | article |
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J. W.</creatorcontrib><creatorcontrib>Meiss, J. D.</creatorcontrib><title>Simultaneous border-collision and period-doubling bifurcations</title><title>Chaos (Woodbury, N.Y.)</title><addtitle>Chaos</addtitle><description>We unfold the codimension-two simultaneous occurrence of a border-collision bifurcation and a period-doubling bifurcation for a general piecewise-smooth, continuous map. We find that with sufficient nondegeneracy conditions, a locus of period-doubling bifurcations emanates nontangentially from a locus of border-collision bifurcations. The corresponding period-doubled solution undergoes a border-collision bifurcation along a curve emanating from the codimension-two point and tangent to the period-doubling locus here. 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D.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Simultaneous border-collision and period-doubling bifurcations</atitle><jtitle>Chaos (Woodbury, N.Y.)</jtitle><addtitle>Chaos</addtitle><date>2009-09-01</date><risdate>2009</risdate><volume>19</volume><issue>3</issue><spage>033146</spage><epage>033146-11</epage><pages>033146-033146-11</pages><issn>1054-1500</issn><eissn>1089-7682</eissn><coden>CHAOEH</coden><abstract>We unfold the codimension-two simultaneous occurrence of a border-collision bifurcation and a period-doubling bifurcation for a general piecewise-smooth, continuous map. We find that with sufficient nondegeneracy conditions, a locus of period-doubling bifurcations emanates nontangentially from a locus of border-collision bifurcations. The corresponding period-doubled solution undergoes a border-collision bifurcation along a curve emanating from the codimension-two point and tangent to the period-doubling locus here. 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| fulltext | fulltext |
| identifier | ISSN: 1054-1500 |
| ispartof | Chaos (Woodbury, N.Y.), 2009-09, Vol.19 (3), p.033146-033146-11 |
| issn | 1054-1500 1089-7682 |
| language | eng |
| recordid | cdi_crossref_primary_10_1063_1_3227645 |
| source | American Institute of Physics:Jisc Collections:Transitional Journals Agreement 2021-23 (Reading list) |
| subjects | Algorithms Computer Simulation Models, Statistical Nonlinear Dynamics Oscillometry - methods |
| title | Simultaneous border-collision and period-doubling bifurcations |
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