Premium
Stability of discrete‐time fractional‐order time‐delayed neural networks in complex field
Author(s) -
Pratap Anbalagan,
Raja Ramachandran,
Cao Jinde,
Huang Chuangxia,
Niezabitowski Michal,
Bagdasar Ovidiu
Publication year - 2020
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.6745
Subject(s) - mathematics , discrete time and continuous time , laplace transform , stability (learning theory) , artificial neural network , mittag leffler function , fractional calculus , correctness , function (biology) , lyapunov function , order (exchange) , control theory (sociology) , mathematical analysis , algorithm , computer science , control (management) , artificial intelligence , statistics , physics , finance , nonlinear system , quantum mechanics , machine learning , evolutionary biology , biology , economics
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.