Shilnikov chaos, Filippov sliding and boundary equilibrium bifurcations
2018 ◽
Vol 29
(5)
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pp. 757-777
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Keyword(s):
In the 1960s, L.P. Shilnikov showed that certain homoclinic orbits for smooth families of differential equations imply the existence of chaos, and there are complicated sequences of bifurcations near the parameter value at which the homoclinic orbit exists. We describe how this analysis is modified if the differential equations are piecewise smooth and the homoclinic orbit has a sliding segment. Moreover, we show that the Shilnikov mechanism appears naturally in the unfolding of boundary equilibrium bifurcations in $\mathbb{R}^3$.
2009 ◽
Vol 139
(1)
◽
pp. 123-155
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2015 ◽
Vol 25
(09)
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pp. 1550114
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Keyword(s):
1997 ◽
Vol 07
(01)
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pp. 27-37
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2000 ◽
Vol 24
(3)
◽
pp. 187-192
Keyword(s):
2017 ◽
Vol 445
(1)
◽
pp. 631-649
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2008 ◽
Vol 27
(1-2)
◽
pp. 107-116
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2017 ◽
Vol 217
◽
pp. 43-57
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1999 ◽
Vol 21
(2)
◽
pp. 591-619
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1996 ◽
Vol 06
(05)
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pp. 867-887
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