Finite Time Synchronization of Extended Nonlinear Dynamical Systems Using Local Coupling
We consider two reaction-diffusion equations connected by one-directional coupling function and study the synchronization problem in the case where the coupling function affects the driven system in some specific regions. We derive conditions that ensure that the evolution of the driven system close...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2017-01-01
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| Series: | International Journal of Differential Equations |
| Online Access: | http://dx.doi.org/10.1155/2017/1946304 |
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| _version_ | 1832548924092579840 |
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| author | A. Acosta P. García H. Leiva A. Merlitti |
| author_facet | A. Acosta P. García H. Leiva A. Merlitti |
| author_sort | A. Acosta |
| collection | DOAJ |
| description | We consider two reaction-diffusion equations connected by one-directional coupling function and study the synchronization problem in the case where the coupling function affects the driven system in some specific regions. We derive conditions that ensure that the evolution of the driven system closely tracks the evolution of the driver system at least for a finite time. The framework built to achieve our results is based on the study of an abstract ordinary differential equation in a suitable Hilbert space. As a specific application we consider the Gray-Scott equations and perform numerical simulations that are consistent with our main theoretical results. |
| format | Article |
| id | doaj-art-da543ff4169346179ad8affce9e8b879 |
| institution | Kabale University |
| issn | 1687-9643 1687-9651 |
| language | English |
| publishDate | 2017-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Differential Equations |
| spelling | doaj-art-da543ff4169346179ad8affce9e8b8792025-02-03T06:12:41ZengWileyInternational Journal of Differential Equations1687-96431687-96512017-01-01201710.1155/2017/19463041946304Finite Time Synchronization of Extended Nonlinear Dynamical Systems Using Local CouplingA. Acosta0P. García1H. Leiva2A. Merlitti3School of Mathematical Sciences and Information Technology, Department of Mathematics, Yachay Tech, Urcuqui, EcuadorFacultad de Ingeniería en Ciencias Aplicadas, Universidad Técnica del Norte, Ibarra, EcuadorSchool of Mathematical Sciences and Information Technology, Department of Mathematics, Yachay Tech, Urcuqui, EcuadorDepartamento de Estadística, Facultad de Ciencias Económicas y Sociales, Universidad Central de Venezuela, Caracas, VenezuelaWe consider two reaction-diffusion equations connected by one-directional coupling function and study the synchronization problem in the case where the coupling function affects the driven system in some specific regions. We derive conditions that ensure that the evolution of the driven system closely tracks the evolution of the driver system at least for a finite time. The framework built to achieve our results is based on the study of an abstract ordinary differential equation in a suitable Hilbert space. As a specific application we consider the Gray-Scott equations and perform numerical simulations that are consistent with our main theoretical results.http://dx.doi.org/10.1155/2017/1946304 |
| spellingShingle | A. Acosta P. García H. Leiva A. Merlitti Finite Time Synchronization of Extended Nonlinear Dynamical Systems Using Local Coupling International Journal of Differential Equations |
| title | Finite Time Synchronization of Extended Nonlinear Dynamical Systems Using Local Coupling |
| title_full | Finite Time Synchronization of Extended Nonlinear Dynamical Systems Using Local Coupling |
| title_fullStr | Finite Time Synchronization of Extended Nonlinear Dynamical Systems Using Local Coupling |
| title_full_unstemmed | Finite Time Synchronization of Extended Nonlinear Dynamical Systems Using Local Coupling |
| title_short | Finite Time Synchronization of Extended Nonlinear Dynamical Systems Using Local Coupling |
| title_sort | finite time synchronization of extended nonlinear dynamical systems using local coupling |
| url | http://dx.doi.org/10.1155/2017/1946304 |
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