Quasi-Matrix and Quasi-Inverse-Matrix Projective Synchronization for Delayed and Disturbed Fractional Order Neural Network
This paper is concerned with the quasi-matrix and quasi-inverse-matrix projective synchronization between two nonidentical delayed fractional order neural networks subjected to external disturbances. First, the definitions of quasi-matrix and quasi-inverse-matrix projective synchronization are given...
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| Format: | Article |
| Language: | English |
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Wiley
2019-01-01
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| Series: | Complexity |
| Online Access: | http://dx.doi.org/10.1155/2019/4823709 |
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| author | Jinman He Fangqi Chen Qinsheng Bi |
| author_facet | Jinman He Fangqi Chen Qinsheng Bi |
| author_sort | Jinman He |
| collection | DOAJ |
| description | This paper is concerned with the quasi-matrix and quasi-inverse-matrix projective synchronization between two nonidentical delayed fractional order neural networks subjected to external disturbances. First, the definitions of quasi-matrix and quasi-inverse-matrix projective synchronization are given, respectively. Then, in order to realize two types of synchronization for delayed and disturbed fractional order neural networks, two sufficient conditions are established and proved by constructing appropriate Lyapunov function in combination with some fractional order differential inequalities. And their estimated synchronization error bound is obtained, which can be reduced to the required standard as small as what we need by selecting appropriate control parameters. Because of the generality of the proposed synchronization, choosing different projective matrix and controllers, the two synchronization types can be reduced to some common synchronization types for delayed fractional order neural networks, like quasi-complete synchronization, quasi-antisynchronization, quasi-projective synchronization, quasi-inverse projective synchronization, quasi-modified projective synchronization, quasi-inverse-modified projective synchronization, and so on. Finally, as applications, two numerical examples with simulations are employed to illustrate the efficiency and feasibility of the new synchronization analysis. |
| format | Article |
| id | doaj-art-a9dfe579e88a41c1a3356d8f9b83656d |
| institution | Kabale University |
| issn | 1076-2787 1099-0526 |
| language | English |
| publishDate | 2019-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Complexity |
| spelling | doaj-art-a9dfe579e88a41c1a3356d8f9b83656d2025-02-03T01:30:59ZengWileyComplexity1076-27871099-05262019-01-01201910.1155/2019/48237094823709Quasi-Matrix and Quasi-Inverse-Matrix Projective Synchronization for Delayed and Disturbed Fractional Order Neural NetworkJinman He0Fangqi Chen1Qinsheng Bi2Department of Mechanics, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, ChinaDepartment of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, ChinaFaculty of Civil Engineering and Mechanics, Jiangsu University, Zhenjiang 212013, ChinaThis paper is concerned with the quasi-matrix and quasi-inverse-matrix projective synchronization between two nonidentical delayed fractional order neural networks subjected to external disturbances. First, the definitions of quasi-matrix and quasi-inverse-matrix projective synchronization are given, respectively. Then, in order to realize two types of synchronization for delayed and disturbed fractional order neural networks, two sufficient conditions are established and proved by constructing appropriate Lyapunov function in combination with some fractional order differential inequalities. And their estimated synchronization error bound is obtained, which can be reduced to the required standard as small as what we need by selecting appropriate control parameters. Because of the generality of the proposed synchronization, choosing different projective matrix and controllers, the two synchronization types can be reduced to some common synchronization types for delayed fractional order neural networks, like quasi-complete synchronization, quasi-antisynchronization, quasi-projective synchronization, quasi-inverse projective synchronization, quasi-modified projective synchronization, quasi-inverse-modified projective synchronization, and so on. Finally, as applications, two numerical examples with simulations are employed to illustrate the efficiency and feasibility of the new synchronization analysis.http://dx.doi.org/10.1155/2019/4823709 |
| spellingShingle | Jinman He Fangqi Chen Qinsheng Bi Quasi-Matrix and Quasi-Inverse-Matrix Projective Synchronization for Delayed and Disturbed Fractional Order Neural Network Complexity |
| title | Quasi-Matrix and Quasi-Inverse-Matrix Projective Synchronization for Delayed and Disturbed Fractional Order Neural Network |
| title_full | Quasi-Matrix and Quasi-Inverse-Matrix Projective Synchronization for Delayed and Disturbed Fractional Order Neural Network |
| title_fullStr | Quasi-Matrix and Quasi-Inverse-Matrix Projective Synchronization for Delayed and Disturbed Fractional Order Neural Network |
| title_full_unstemmed | Quasi-Matrix and Quasi-Inverse-Matrix Projective Synchronization for Delayed and Disturbed Fractional Order Neural Network |
| title_short | Quasi-Matrix and Quasi-Inverse-Matrix Projective Synchronization for Delayed and Disturbed Fractional Order Neural Network |
| title_sort | quasi matrix and quasi inverse matrix projective synchronization for delayed and disturbed fractional order neural network |
| url | http://dx.doi.org/10.1155/2019/4823709 |
| work_keys_str_mv | AT jinmanhe quasimatrixandquasiinversematrixprojectivesynchronizationfordelayedanddisturbedfractionalorderneuralnetwork AT fangqichen quasimatrixandquasiinversematrixprojectivesynchronizationfordelayedanddisturbedfractionalorderneuralnetwork AT qinshengbi quasimatrixandquasiinversematrixprojectivesynchronizationfordelayedanddisturbedfractionalorderneuralnetwork |