Global Mittag—Leffler Synchronization for Neural Networks Modeled by Impulsive Caputo Fractional Differential Equations with Distributed Delays
The synchronization problem for impulsive fractional-order neural networks with both time-varying bounded and distributed delays is studied. We study the case when the neural networks and the fractional derivatives of all neurons depend significantly on the moments of impulses and we consider both t...
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MDPI AG
2018-10-01
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| Series: | Symmetry |
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| Online Access: | http://www.mdpi.com/2073-8994/10/10/473 |
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doaj-f2c9a3ff17944bdeba37e48c311dda632020-11-25T00:17:36ZengMDPI AGSymmetry2073-89942018-10-01101047310.3390/sym10100473sym10100473Global Mittag—Leffler Synchronization for Neural Networks Modeled by Impulsive Caputo Fractional Differential Equations with Distributed DelaysRavi Agarwal0Snezhana Hristova1Donal O’Regan2Department of Mathematics, Texas A&M University-Kingsville, Kingsville, TX 78363, USADepartment of Applied Mathematics and Modeling, University of Plovdiv, Tzar Asen 24, 4000 Plovdiv, BulgariaSchool of Mathematics, Statistics and Applied Mathematics, National University of Ireland, H91 CF50 Galway, IrelandThe synchronization problem for impulsive fractional-order neural networks with both time-varying bounded and distributed delays is studied. We study the case when the neural networks and the fractional derivatives of all neurons depend significantly on the moments of impulses and we consider both the cases of state coupling controllers and output coupling controllers. The fractional generalization of the Razumikhin method and Lyapunov functions is applied. Initially, a brief overview of the basic fractional derivatives of Lyapunov functions used in the literature is given. Some sufficient conditions are derived to realize the global Mittag–Leffler synchronization of impulsive fractional-order neural networks. Our results are illustrated with examples.http://www.mdpi.com/2073-8994/10/10/473fractional-order neural networksdelaysdistributed delaysimpulsesMittag–Leffler synchronizationLyapunov functionsRazumikhin method |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Ravi Agarwal Snezhana Hristova Donal O’Regan |
| spellingShingle |
Ravi Agarwal Snezhana Hristova Donal O’Regan Global Mittag—Leffler Synchronization for Neural Networks Modeled by Impulsive Caputo Fractional Differential Equations with Distributed Delays Symmetry fractional-order neural networks delays distributed delays impulses Mittag–Leffler synchronization Lyapunov functions Razumikhin method |
| author_facet |
Ravi Agarwal Snezhana Hristova Donal O’Regan |
| author_sort |
Ravi Agarwal |
| title |
Global Mittag—Leffler Synchronization for Neural Networks Modeled by Impulsive Caputo Fractional Differential Equations with Distributed Delays |
| title_short |
Global Mittag—Leffler Synchronization for Neural Networks Modeled by Impulsive Caputo Fractional Differential Equations with Distributed Delays |
| title_full |
Global Mittag—Leffler Synchronization for Neural Networks Modeled by Impulsive Caputo Fractional Differential Equations with Distributed Delays |
| title_fullStr |
Global Mittag—Leffler Synchronization for Neural Networks Modeled by Impulsive Caputo Fractional Differential Equations with Distributed Delays |
| title_full_unstemmed |
Global Mittag—Leffler Synchronization for Neural Networks Modeled by Impulsive Caputo Fractional Differential Equations with Distributed Delays |
| title_sort |
global mittag—leffler synchronization for neural networks modeled by impulsive caputo fractional differential equations with distributed delays |
| publisher |
MDPI AG |
| series |
Symmetry |
| issn |
2073-8994 |
| publishDate |
2018-10-01 |
| description |
The synchronization problem for impulsive fractional-order neural networks with both time-varying bounded and distributed delays is studied. We study the case when the neural networks and the fractional derivatives of all neurons depend significantly on the moments of impulses and we consider both the cases of state coupling controllers and output coupling controllers. The fractional generalization of the Razumikhin method and Lyapunov functions is applied. Initially, a brief overview of the basic fractional derivatives of Lyapunov functions used in the literature is given. Some sufficient conditions are derived to realize the global Mittag–Leffler synchronization of impulsive fractional-order neural networks. Our results are illustrated with examples. |
| topic |
fractional-order neural networks delays distributed delays impulses Mittag–Leffler synchronization Lyapunov functions Razumikhin method |
| url |
http://www.mdpi.com/2073-8994/10/10/473 |
| work_keys_str_mv |
AT raviagarwal globalmittaglefflersynchronizationforneuralnetworksmodeledbyimpulsivecaputofractionaldifferentialequationswithdistributeddelays AT snezhanahristova globalmittaglefflersynchronizationforneuralnetworksmodeledbyimpulsivecaputofractionaldifferentialequationswithdistributeddelays AT donaloregan globalmittaglefflersynchronizationforneuralnetworksmodeledbyimpulsivecaputofractionaldifferentialequationswithdistributeddelays |
| _version_ |
1725378929519230976 |