BORDER-COLLISION BIFURCATIONS IN 1D PIECEWISE-LINEAR MAPS AND LEONOV'S APPROACH
2010 ◽
Vol 20
(10)
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pp. 3085-3104
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Keyword(s):
50 years ago (1959) in a series of publications by Leonov, a detailed analytical study of the nested period adding bifurcation structure occurring in piecewise-linear discontinuous 1D maps was presented. The results obtained by Leonov are barely known, although they allow the analytical calculation of border-collision bifurcation subspaces in an elegant and much more efficient way than it is usually done. In this work we recall Leonov's approach and explain why it works. Furthermore, we slightly improve the approach by avoiding an unnecessary coordinate transformation, and also demonstrate that the approach can be used not only for the calculation of border-collision bifurcation curves.
2014 ◽
Vol 19
(8)
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pp. 2771-2784
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2020 ◽
Vol 30
(03)
◽
pp. 2030006
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2012 ◽
Vol 22
(03)
◽
pp. 1250068
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2020 ◽
Vol 80
(3)
◽
pp. 1356-1376
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Keyword(s):
2010 ◽
Vol 20
(10)
◽
pp. 3105-3135
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Keyword(s):
1997 ◽
Vol 07
(07)
◽
pp. 1617-1634
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