Dynamics of the system of delay differential equations with nonlinearity having a simple behavior at infinity
In this paper, we study the dynamics of a system of nonlinear differential equations with delay. We find stable equilibrium states and regions of attraction to them in the phase space of the system, as well as stable and unstable homogeneous and inhomogeneous cycles. We find conditions on the parame...
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| Format: | Article |
| Language: | English |
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Elsevier
2024-12-01
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| Series: | Partial Differential Equations in Applied Mathematics |
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| Online Access: | http://www.sciencedirect.com/science/article/pii/S2666818124003206 |
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| author | A.A. Kashchenko I.S. Luzin |
| author_facet | A.A. Kashchenko I.S. Luzin |
| author_sort | A.A. Kashchenko |
| collection | DOAJ |
| description | In this paper, we study the dynamics of a system of nonlinear differential equations with delay. We find stable equilibrium states and regions of attraction to them in the phase space of the system, as well as stable and unstable homogeneous and inhomogeneous cycles. We find conditions on the parameters of the system for multistability. We show that the coupling parameter has a decisive influence on the dynamics of the system. We find regions of the parameters of the system and extensive sets of initial conditions such that if we take these values of the parameters and any initial conditions from these sets, the system will have simple dynamics. |
| format | Article |
| id | doaj-art-ad1ccc19cf3d427f82771bb1d503b2da |
| institution | DOAJ |
| issn | 2666-8181 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Partial Differential Equations in Applied Mathematics |
| spelling | doaj-art-ad1ccc19cf3d427f82771bb1d503b2da2025-08-20T02:50:13ZengElsevierPartial Differential Equations in Applied Mathematics2666-81812024-12-011210093410.1016/j.padiff.2024.100934Dynamics of the system of delay differential equations with nonlinearity having a simple behavior at infinityA.A. Kashchenko0I.S. Luzin1Corresponding author.; Centre of Integrable Systems, P.G. Demidov Yaroslavl State University, Sovetskaya ul., 14, Yaroslavl, 150003, RussiaCentre of Integrable Systems, P.G. Demidov Yaroslavl State University, Sovetskaya ul., 14, Yaroslavl, 150003, RussiaIn this paper, we study the dynamics of a system of nonlinear differential equations with delay. We find stable equilibrium states and regions of attraction to them in the phase space of the system, as well as stable and unstable homogeneous and inhomogeneous cycles. We find conditions on the parameters of the system for multistability. We show that the coupling parameter has a decisive influence on the dynamics of the system. We find regions of the parameters of the system and extensive sets of initial conditions such that if we take these values of the parameters and any initial conditions from these sets, the system will have simple dynamics.http://www.sciencedirect.com/science/article/pii/S2666818124003206DelayMultistabilityCycleAsymptoticsNonlocal dynamics |
| spellingShingle | A.A. Kashchenko I.S. Luzin Dynamics of the system of delay differential equations with nonlinearity having a simple behavior at infinity Partial Differential Equations in Applied Mathematics Delay Multistability Cycle Asymptotics Nonlocal dynamics |
| title | Dynamics of the system of delay differential equations with nonlinearity having a simple behavior at infinity |
| title_full | Dynamics of the system of delay differential equations with nonlinearity having a simple behavior at infinity |
| title_fullStr | Dynamics of the system of delay differential equations with nonlinearity having a simple behavior at infinity |
| title_full_unstemmed | Dynamics of the system of delay differential equations with nonlinearity having a simple behavior at infinity |
| title_short | Dynamics of the system of delay differential equations with nonlinearity having a simple behavior at infinity |
| title_sort | dynamics of the system of delay differential equations with nonlinearity having a simple behavior at infinity |
| topic | Delay Multistability Cycle Asymptotics Nonlocal dynamics |
| url | http://www.sciencedirect.com/science/article/pii/S2666818124003206 |
| work_keys_str_mv | AT aakashchenko dynamicsofthesystemofdelaydifferentialequationswithnonlinearityhavingasimplebehavioratinfinity AT isluzin dynamicsofthesystemofdelaydifferentialequationswithnonlinearityhavingasimplebehavioratinfinity |