Stability analysis of neural networks with piecewise constant argument

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Tezin Türü: Doktora

Tezin Yürütüldüğü Kurum: Orta Doğu Teknik Üniversitesi, Fen Edebiyat Fakültesi, Matematik Bölümü, Türkiye

Tezin Onay Tarihi: 2017

Tezin Dili: İngilizce

Öğrenci: MELTEM KARACAÖREN

Danışman: Marat Akhmet

Özet:

Last several decades, an immense attention has been paid to the construction and analysis of neural networks since it is related to the brain activity. One of the most important neural networks is Hopfield neural network. Since it is obtained from the direct modeling of neuron activity, the results of the research have effective consequences for the modern science. Dynamical analysis of Hopfield neural networks concerns to the method of qualitative theory of differential equations. In particular, it relates to the existence and stability of oscillatory solutions, equilibrium, periodic and almost periodic solutions. Due to the significance of the Hopfield neural networks, one must modernize the models to satisfy the present and potential applications in neuroscience and other fields of the modern research. This is why in the present thesis, we have developed the Hopfield’s model by inserting piecewise constant argument of generalized type which is started to be considered in the theory of differential equations several years ago in 2005. The new models contain piecewise constant argument and constant delays. We investigate the sufficient conditions for existence and uniqueness of solutions, global exponential stability of equilibrium points for these neural networks. By means of Lyapunov functionals, the conditions for stability and linear matrix inequality method have been obtained.