### Abstract

Several aspects of global dynamics and the existence of periodic solutions are studied for the scalar differential delay equation x′(t) = a(t)f(x([t - K])), where f(x) is a continuous negative feedback function, x · f(x) < 0, x ≠ 0, 0 < a(t) is continuous ω-periodic, [·] is the integer part function, and the integer K ≥ 0 is the delay. The case of integer period x allows for a reduction to finite-dimensional difference equations. The dynamics of the latter are studied in terms of corresponding discrete maps, including the partial case of interval maps (K = 0).

Original language | English (US) |
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Pages (from-to) | 446-456 |

Number of pages | 11 |

Journal | Applied Mathematics and Computation |

Volume | 252 |

DOIs | |

State | Published - Feb 1 2015 |

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### All Science Journal Classification (ASJC) codes

- Computational Mathematics
- Applied Mathematics

### Cite this

*Applied Mathematics and Computation*,

*252*, 446-456. https://doi.org/10.1016/j.amc.2014.12.015

}

*Applied Mathematics and Computation*, vol. 252, pp. 446-456. https://doi.org/10.1016/j.amc.2014.12.015

**On global dynamics in a periodic differential equation with deviating argument.** / Ivanov, Anatoli; Trofimchuk, Sergei I.

Research output: Contribution to journal › Article

TY - JOUR

T1 - On global dynamics in a periodic differential equation with deviating argument

AU - Ivanov, Anatoli

AU - Trofimchuk, Sergei I.

PY - 2015/2/1

Y1 - 2015/2/1

N2 - Several aspects of global dynamics and the existence of periodic solutions are studied for the scalar differential delay equation x′(t) = a(t)f(x([t - K])), where f(x) is a continuous negative feedback function, x · f(x) < 0, x ≠ 0, 0 < a(t) is continuous ω-periodic, [·] is the integer part function, and the integer K ≥ 0 is the delay. The case of integer period x allows for a reduction to finite-dimensional difference equations. The dynamics of the latter are studied in terms of corresponding discrete maps, including the partial case of interval maps (K = 0).

AB - Several aspects of global dynamics and the existence of periodic solutions are studied for the scalar differential delay equation x′(t) = a(t)f(x([t - K])), where f(x) is a continuous negative feedback function, x · f(x) < 0, x ≠ 0, 0 < a(t) is continuous ω-periodic, [·] is the integer part function, and the integer K ≥ 0 is the delay. The case of integer period x allows for a reduction to finite-dimensional difference equations. The dynamics of the latter are studied in terms of corresponding discrete maps, including the partial case of interval maps (K = 0).

UR - http://www.scopus.com/inward/record.url?scp=84920193218&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84920193218&partnerID=8YFLogxK

U2 - 10.1016/j.amc.2014.12.015

DO - 10.1016/j.amc.2014.12.015

M3 - Article

VL - 252

SP - 446

EP - 456

JO - Applied Mathematics and Computation

JF - Applied Mathematics and Computation

SN - 0096-3003

ER -