Stability of discrete-time fractional-order time-delayed neural networks in complex field
Journal article
Pratap, Anbalagan, Raja, Ramachandran, Cao, Jinde, Huang, Chuangxia, Niezabitowski, Michal and Bagdasar, Ovidiu 2020. Stability of discrete-time fractional-order time-delayed neural networks in complex field. Mathematical Methods in the Applied Sciences. https://doi.org/10.1002/mma.6745
| Authors | Pratap, Anbalagan, Raja, Ramachandran, Cao, Jinde, Huang, Chuangxia, Niezabitowski, Michal and Bagdasar, Ovidiu |
|---|---|
| Abstract | Dynamics of discrete‐time neural networks have not been well documented yet in fractional‐order cases, which is the first time documented in this manuscript. This manuscript is mainly considered on the stability criterion of discrete‐time fractional‐order complex‐valued neural networks with time delays. When the fractional‐order β holds 1 < β < 2, sufficient criteria based on a discrete version of generalized Gronwall inequality and rising function property are established for ensuring the finite stability of addressing fractional‐order discrete‐time‐delayed complex‐valued neural networks (FODCVNNs). In the meanwhile, when the fractional‐order β holds 0 < β < 1, a global Mittag–Leffler stability criterion of a class of FODCVNNs is demonstrated with two classes of neuron activation function by means of two different new inequalities, fractional‐order discrete‐time Lyapunov method, discrete version Laplace transforms as well as a discrete version of Mittag–Leffler function. Finally, computer simulations of two numerical examples are illustrated to the correctness and effectiveness of the presented stability results. |
| Keywords | General Engineering; General Mathematics; neural networks; Research Subject Categories::MATHEMATICS; Research Subject Categories::MATHEMATICS::Applied mathematics::Theoretical computer science |
| Year | 2020 |
| Journal | Mathematical Methods in the Applied Sciences |
| Publisher | Wiley |
| ISSN | 0170-4214 |
| Digital Object Identifier (DOI) | https://doi.org/10.1002/mma.6745 |
| Web address (URL) | http://hdl.handle.net/10545/625159 |
| http://doi.wiley.com/10.1002/tdm_license_1.1 | |
| hdl:10545/625159 | |
| Publication dates | 30 Jul 2020 |
| Publication process dates | |
| Deposited | 16 Sep 2020, 09:21 |
| Accepted | 06 Jul 2020 |
| Contributors | Alagappa University, Karaikudi, India, Southeast University, Nanjing, China, Changsha University of Science and Technology, Changsha 410114, China, University of Technology, Gliwice, Poland and University of Derby |
| File | File Access Level Open |
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Bagdasar, Ovidiu and Larcombe, Peter J. 2013. On the number of complex horadam sequences with a fixed period. Fibonacci Quarterly.On the characterization of periodic complex Horadam sequences
Bagdasar, Ovidiu and Larcombe, Peter J. 2013. On the characterization of periodic complex Horadam sequences. Fibonacci Quarterly.On a result of Bunder involving Horadam sequences: A proof and generalization
Larcombe, Peter J. and Bagdasar, Ovidiu 2013. On a result of Bunder involving Horadam sequences: A proof and generalization. Fibonacci Quarterly.Influence discovery in semantic networks: An initial approach
Trovati, M. and Bagdasar, O. 2014. Influence discovery in semantic networks: An initial approach. IEEE. https://doi.org/10.1109/uksim.2014.48Complementary iInequalities involving the Stolarsky Mean
Bagdasar, Ovidiu 2010. Complementary iInequalities involving the Stolarsky Mean. Journal of Inequalities and Applications. https://doi.org/10.1155/2010/492570Concise computer mathematics: tutorials on theory and problems
Bagdasar, Ovidiu 2013. Concise computer mathematics: tutorials on theory and problems. Springer.On the characterization of periodic generalized Horadam sequences
Bagdasar, Ovidiu and Larcombe, Peter J. 2014. On the characterization of periodic generalized Horadam sequences. Journal of Difference Equations and Applications. https://doi.org/10.1080/10236198.2014.891022Local maximum points of explicitly quasiconvex functions
Bagdasar, Ovidiu and Popovici, Nicolae 2014. Local maximum points of explicitly quasiconvex functions. Optimization Letters. https://doi.org/10.1007/s11590-014-0781-3A horadam-based pseudo-random number generator
Bagdasar, O.D., Chen, M. and Bagdasar, O. 2014. A horadam-based pseudo-random number generator. IEEE. https://doi.org/10.1109/uksim.2014.55On the structure of periodic complex Horadam orbits
Bagdasar, Ovidiu D., Larcombe, Peter J., Anjum, Ashiq and Bagdasar, O. 2016. On the structure of periodic complex Horadam orbits. Carpathian Journal of Mathematics.Characterizations of Generalized Exponential Trichotomies for Linear Discrete-time Systems
Popa, I.-L., Ceauşu, T., Bagdasar, O. and Agarwal, R.P. 2016. Characterizations of Generalized Exponential Trichotomies for Linear Discrete-time Systems. Analele Stiintifice ale Universitatii Ovidius Constanta, Seria Matematica. 27 (2), pp. 153-166. https://doi.org/10.2478/auom-2019-0025On some functions involving the lcm and gcd of integer tuples
Bagdasar, Ovidiu 2014. On some functions involving the lcm and gcd of integer tuples. Scientific Publications of the State University of Novi Pazar Series A: Applied Mathematics, Informatics and mechanics. https://doi.org/10.5937/SPSUNP1402091B