Dependence of Dynamics of a System of Two Coupled Generators with Delayed Feedback on the Sign of Coupling
In this paper, we study the nonlocal dynamics of a system of delay differential equations with large parameters. This system simulates coupled generators with delayed feedback. Using the method of steps, we construct asymptotics of solutions. By these asymptotics, we construct a special finite-dimen...
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| Format: | Article |
| Language: | English |
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MDPI AG
2020-10-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/8/10/1790 |
| _version_ | 1797550901186002944 |
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| author | Alexandra Kashchenko |
| author_facet | Alexandra Kashchenko |
| author_sort | Alexandra Kashchenko |
| collection | DOAJ |
| description | In this paper, we study the nonlocal dynamics of a system of delay differential equations with large parameters. This system simulates coupled generators with delayed feedback. Using the method of steps, we construct asymptotics of solutions. By these asymptotics, we construct a special finite-dimensional map. This map helps us to determine the structure of solutions. We study the dependence of solutions on the coupling parameter and show that the dynamics of the system is significantly different in the case of positive coupling and in the case of negative coupling. |
| first_indexed | 2024-03-10T15:36:59Z |
| format | Article |
| id | doaj.art-eefe87e327294f14ab451077338e6684 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T15:36:59Z |
| publishDate | 2020-10-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-eefe87e327294f14ab451077338e66842023-11-20T17:13:19ZengMDPI AGMathematics2227-73902020-10-01810179010.3390/math8101790Dependence of Dynamics of a System of Two Coupled Generators with Delayed Feedback on the Sign of CouplingAlexandra Kashchenko0Mathematical Department, P.G. Demidov Yaroslavl State University, Yaroslavl 150003, RussiaIn this paper, we study the nonlocal dynamics of a system of delay differential equations with large parameters. This system simulates coupled generators with delayed feedback. Using the method of steps, we construct asymptotics of solutions. By these asymptotics, we construct a special finite-dimensional map. This map helps us to determine the structure of solutions. We study the dependence of solutions on the coupling parameter and show that the dynamics of the system is significantly different in the case of positive coupling and in the case of negative coupling.https://www.mdpi.com/2227-7390/8/10/1790relaxation modedelay differential equationlarge parameterasymptotics |
| spellingShingle | Alexandra Kashchenko Dependence of Dynamics of a System of Two Coupled Generators with Delayed Feedback on the Sign of Coupling Mathematics relaxation mode delay differential equation large parameter asymptotics |
| title | Dependence of Dynamics of a System of Two Coupled Generators with Delayed Feedback on the Sign of Coupling |
| title_full | Dependence of Dynamics of a System of Two Coupled Generators with Delayed Feedback on the Sign of Coupling |
| title_fullStr | Dependence of Dynamics of a System of Two Coupled Generators with Delayed Feedback on the Sign of Coupling |
| title_full_unstemmed | Dependence of Dynamics of a System of Two Coupled Generators with Delayed Feedback on the Sign of Coupling |
| title_short | Dependence of Dynamics of a System of Two Coupled Generators with Delayed Feedback on the Sign of Coupling |
| title_sort | dependence of dynamics of a system of two coupled generators with delayed feedback on the sign of coupling |
| topic | relaxation mode delay differential equation large parameter asymptotics |
| url | https://www.mdpi.com/2227-7390/8/10/1790 |
| work_keys_str_mv | AT alexandrakashchenko dependenceofdynamicsofasystemoftwocoupledgeneratorswithdelayedfeedbackonthesignofcoupling |