Necessary and Sufficient Conditions for the Occurrence of Bisecting Bifurcations in the General 2D Piecewise-Linear Mapping
2017 ◽
Vol 27
(05)
◽
pp. 1750079
Keyword(s):
In this work, we focus on the conditions for the occurrence of a special type of bifurcations in the general 2D piecewise-linear mapping called bisecting bifurcations. This kind of bifurcation is mediated by an infinite set of neutrally stable periodic orbits, i.e. cycles with multiplier unity. We used the definition of the rank of both coefficient and augmented matrices based on minors to find the necessary and sufficient conditions in which the bisecting bifurcation occurs.
2011 ◽
Vol 2011
◽
pp. 1-19
◽
1998 ◽
Vol 18
(5)
◽
pp. 1097-1114
◽
1975 ◽
Vol 18
(1)
◽
pp. 7-17
◽
1978 ◽
Vol 30
(4)
◽
pp. 783-796
◽
2006 ◽
Vol 2006
◽
pp. 1-13
2013 ◽
Vol 336-338
◽
pp. 2359-2362
2015 ◽
Vol 23
(03)
◽
pp. 367-377