Analysis of neural network models of integer and non-integer order (PhD)

Abstract

The present thesis deals with the investigation of more interesting dynamics in various generalized models of artificial delayed neural networks of both integer order and fractional order. The study provides insight into the detailed stability analysis of the various delayed models, such as existence and uniqueness of solutions to the network models and their stability analysis (Uniform stability, Asymptotic stability, Mittag-Leffer stability etc). We obtain various necessary and sufficient conditions for the existence, uniqueness and stability of the solutions to various delayed differential neural network models in terms of system parameters. The most significant contribution of this thesis is the introduction of a new discretization scheme to approximate the solutions of continuous-time fractional-order delayed neural networks via discrete difference equations, which has not been proposed so far to the best of our knowledge. We have also shown using exponential stability of the solutions that the obtained results are better approximation for the solution to the neural network models. Moreover, we have derived the global Mittag-Leffer stability of a complex valued fractional-order neural network with discrete and distributed time delay, which is quiet remarkable. Furthermore, the stability and synchronization has been investigated for various classes of neural networks, such as impulsive neural networks, projection neural networks, ring neural networks with reaction-diffusion terms. Various results have been derived to analyze the dynamic behaviour of the solutions to these models. The obtained results provide better understanding of the local as well as global behaviour of the various models. Numerical simulations have also been carried out to support the theoretical analysis. The main tools used in this study are fixed point methods, Lyapunov function, generalized Gronwall inequality, Razumikhin technique and fractional Adams-Bashforth- Moulton predictor-corrector numerical scheme.