Border-collision bifurcations in 1D piecewise-linear maps and Leonov's approach

L Gardini, F Tramontana, V Avrutin… - International Journal of …, 2010 - World Scientific
International Journal of Bifurcation and Chaos, 2010World Scientific
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 …
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.
World Scientific
以上显示的是最相近的搜索结果。 查看全部搜索结果