Geodesic
Relaxation oscillations in a~logistic equation with past state-dependent delay
Teoretičeskaâ i matematičeskaâ fizika, Tome 207 (2021) no. 3, pp. 389-402

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A logistic equation with a delay depending on the state in the past is considered. We study the question of the existence of nonlocal relaxation periodic solutions of this equation for large values of the parameter. The characteristics (for example, period and extreme values) of solutions that we find are compared with similar characteristics of solutions of other modifications of this equation. Asymptotic estimates for the period and the maximum and minimum values are obtained. The study is carried out by the large parameter method.
Keywords: delay equation, nonconstant delay, asymptotics, large parameter method.
Mots-clés : relaxation solution 
@article{TMF_2021_207_3_a4,
     author = {V. O. Golubenets},
     title = {Relaxation oscillations in a~logistic equation with past state-dependent delay},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {389--402},
     publisher = {mathdoc},
     volume = {207},
     number = {3},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2021_207_3_a4/}
}
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V. O. Golubenets. Relaxation oscillations in a~logistic equation with past state-dependent delay. Teoretičeskaâ i matematičeskaâ fizika, Tome 207 (2021) no. 3, pp. 389-402. http://geodesic.mathdoc.fr/item/TMF_2021_207_3_a4/