Limiting profiles for periodic solutions of scalar delay differential equations
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Bibliographic record
Abstract
Let f (·, λ) : R→R be given so that f (0, λ) = 0 and f ( x , λ) = (1 + λ) x + ax 2 + bx 3 + o ( x 3 ) 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 + ax 2 + bx 3 + o ( x 3 ) 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.
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| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.002 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
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