Limiting profiles for periodic solutions of scalar delay differential equations
2001 ◽
Vol 131
(4)
◽
pp. 799-810
Keyword(s):
Let f(·, λ) : R→R be given so that f(0, λ) = 0 and f(x, λ) = (1 + λ)x + ax2 + bx3 + o(x3) as x → 0. We characterize those small values of ε > 0 and λ ∈ R for which there are periodic solutions of periods approximately 1/k with k ∈ N of the delay equations When a = 0, these periodic solutions approach square waves if b < 0 or pulses if b > 0 as ε → 0. These results are similar to those obtained by Chow et al. and Hale and Huang, where the case of f(x, λ) = −(1 + λ)x + ax2 + bx3 + o(x3) as x → 0 is considered. However, when a ≠ 0, all these periodic solutions approach pulses as ε → 0; an interesting phenomenon that cannot happen in the case considered by Chow et al. and Hale and Huang.
2009 ◽
Vol 247
(3)
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pp. 822-865
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2007 ◽
Vol 233
(2)
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pp. 404-416
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2008 ◽
Vol 21
(1)
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pp. 45-71
2004 ◽
Vol 16
(3)
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pp. 605-628
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1996 ◽
Vol 48
(4)
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pp. 871-886
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2009 ◽
Vol 10
(5)
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pp. 3285-3297
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