Abstract
Abstract One of the main problems connected with neural networks is synchronization. We examine a model of a neural network with time-varying delay and also the case when the connection weights (the influential strength of the j j th neuron to the i i th neuron) are variable in time and unbounded. The rate of change of the dynamics of all neurons is described by the Caputo fractional derivative. We apply Lyapunov functions and the Razumikhin method to obtain some sufficient conditions to ensure synchronization in the model. These sufficient conditions are explicitly expressed in terms of the parameters of the system, and hence, they are easily verifiable. We illustrate our theory with a particular nonlinear neural network.
Highlights
Nowadays, the synchronization of fractional-order delayed neural networks has attracted more and more attention
Some synchronization results have been obtained, for instance, in [1,2,3], where the authors studied the synchronization of fractional-order memristor-based neural networks with delay
Motivated by the above discussions, the main goal of this paper is to study synchronization of neural networks with delay and with the Caputo fractional derivative
Summary
The synchronization of fractional-order delayed neural networks has attracted more and more attention. Some synchronization results have been obtained, for instance, in [1,2,3], where the authors studied the synchronization of fractional-order memristor-based neural networks with delay. Motivated by the above discussions, the main goal of this paper is to study synchronization of neural networks with delay and with the Caputo fractional derivative. We study the general case of time-varying self-regulating parameters of all units and time-varying functions of the connection between two neurons in the network. In [4] the model is considered in the case all the connection weights are constants, the self-inhibition rate is described by a constant, and for a very special output depending on the Lipschitz constants of the activation functions.
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