Asymptotics of Solutions to a Differential Equation with Delay and Nonlinearity Having Simple Behaviour at Infinity
In this paper, we study nonlocal dynamics of a nonlinear delay differential equation. This equation with different types of nonlinearities appears in medical, physical, biological, and ecological applications. The type of nonlinearity in this paper is a generalization of two important for applicatio...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-09-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/10/18/3360 |
| _version_ | 1797485156188028928 |
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| author | Alexandra Kashchenko |
| author_facet | Alexandra Kashchenko |
| author_sort | Alexandra Kashchenko |
| collection | DOAJ |
| description | In this paper, we study nonlocal dynamics of a nonlinear delay differential equation. This equation with different types of nonlinearities appears in medical, physical, biological, and ecological applications. The type of nonlinearity in this paper is a generalization of two important for applications types of nonlinearities: piecewise constant and compactly supported functions. We study asymptotics of solutions under the condition that nonlinearity is multiplied by a large parameter. We construct all solutions of the equation with initial conditions from a wide subset of the phase space and find conditions on the parameters of equations for having periodic solutions. |
| first_indexed | 2024-03-09T23:15:38Z |
| format | Article |
| id | doaj.art-7a652fac430d49ca9c5852e0e6b5a54b |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-09T23:15:38Z |
| publishDate | 2022-09-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-7a652fac430d49ca9c5852e0e6b5a54b2023-11-23T17:37:26ZengMDPI AGMathematics2227-73902022-09-011018336010.3390/math10183360Asymptotics of Solutions to a Differential Equation with Delay and Nonlinearity Having Simple Behaviour at InfinityAlexandra Kashchenko0Centre of Integrable Systems, P. G. Demidov Yaroslavl State University, 150003 Yaroslavl, RussiaIn this paper, we study nonlocal dynamics of a nonlinear delay differential equation. This equation with different types of nonlinearities appears in medical, physical, biological, and ecological applications. The type of nonlinearity in this paper is a generalization of two important for applications types of nonlinearities: piecewise constant and compactly supported functions. We study asymptotics of solutions under the condition that nonlinearity is multiplied by a large parameter. We construct all solutions of the equation with initial conditions from a wide subset of the phase space and find conditions on the parameters of equations for having periodic solutions.https://www.mdpi.com/2227-7390/10/18/3360delayasymptoticslarge parameterrelaxation oscillationsperiodic solutions |
| spellingShingle | Alexandra Kashchenko Asymptotics of Solutions to a Differential Equation with Delay and Nonlinearity Having Simple Behaviour at Infinity Mathematics delay asymptotics large parameter relaxation oscillations periodic solutions |
| title | Asymptotics of Solutions to a Differential Equation with Delay and Nonlinearity Having Simple Behaviour at Infinity |
| title_full | Asymptotics of Solutions to a Differential Equation with Delay and Nonlinearity Having Simple Behaviour at Infinity |
| title_fullStr | Asymptotics of Solutions to a Differential Equation with Delay and Nonlinearity Having Simple Behaviour at Infinity |
| title_full_unstemmed | Asymptotics of Solutions to a Differential Equation with Delay and Nonlinearity Having Simple Behaviour at Infinity |
| title_short | Asymptotics of Solutions to a Differential Equation with Delay and Nonlinearity Having Simple Behaviour at Infinity |
| title_sort | asymptotics of solutions to a differential equation with delay and nonlinearity having simple behaviour at infinity |
| topic | delay asymptotics large parameter relaxation oscillations periodic solutions |
| url | https://www.mdpi.com/2227-7390/10/18/3360 |
| work_keys_str_mv | AT alexandrakashchenko asymptoticsofsolutionstoadifferentialequationwithdelayandnonlinearityhavingsimplebehaviouratinfinity |