Almost periodic solutions of recurrently structured impulsive neural networks

Top, Gülbahar
This thesis aims to conduct detailed and precise neural networks research with impulses at nonprescribed moments in terms of periodic and almost periodic solutions. Most of the actions in nature modeled by neural networks involve repetitions. Hence periodic and almost periodic motions become crucial. So in this thesis, the existence, uniqueness, and stability of the periodic and almost periodic motion are served for the neural networks with prescribed and nonprescribed impacts. This impulsive system is a neural network with innovative structured impacts that perfectly match the rates. If one regards the impulses as limits of their continuous counterparts, this makes sense for the application. Thus, the novel system also considers the neural networks' nature in the impulsive part since the sudden noises or impact disturbances can affect the rates or activation functions. New conditions on the coefficients have been designed to be more specific and detailed. The constructive stability conditions are delivered directly related to the system's coefficients. A detailed approach is performed to the systems with variable moments of impulses. For the research, the method of B-equivalence is employed, and the relationship between the original and B-equivalent systems was explicitly established and provided. Furthermore, because the impulsive component of the system is inherent to the neural network, the B-equivalent system also matches the original structure in terms of differential and impulsive parts. One of the novel aspects of this work is that the possibility of negative capacitance in a neurological system is not neglected. Together with the elimination of the capacitance's positivity requirement, the new structure allows for a more thorough study under optimal conditions. The probability of negative capacitance emphasizes the need for impulses to maintain stability.


Fen, Mehmet Onur; Akhmet, Marat (2016-06-01)
In the present study, we investigate the dynamics of shunting inhibitory cellular neural networks (SICNNs) with impulsive effects. We give a mathematical description of the chaos for the multidimensional dynamics of impulsive SICNNs, and prove its existence rigorously by taking advantage of the external inputs. The Li-Yorke definition of chaos is used in our theoretical discussions. In the considered model, the impacts satisfy the cell and shunting principles. This enriches the applications of SICNNs and ma...
Almost Periodic Solutions of Recurrently Structured Impulsive Neural Networks
Akhmet, Marat; Erim, Gülbahar (2022-01-01)
©2022 L&H Scientific Publishing, LLC. All rights reserved.The model under discussion is an elaborated recurrent impulsive neural network. This is the first time in literature that the impacts are structured completely as the original neural network, such that physical sense of impacts has been explained. Moreover, the impact part comprises all types of impacts in neural networks, which were traditionally studied in conservative models. In the research, neuron membranes with negative as well as positive capa...
Periodic solution for state-dependent impulsive shunting inhibitory CNNs with time-varying delays
Sayli, Mustafa; YILMAZ, ENES (2015-08-01)
In this paper, we consider existence and global exponential stability of periodic solution for state-dependent impulsive shunting inhibitory cellular neural networks with time-varying delays. By means of B-equivalence method, we reduce these state-dependent impulsive neural networks system to an equivalent fix time impulsive neural networks system. Further, by using Mawhin's continuation theorem of coincide degree theory and employing a suitable Lyapunov function some new sufficient conditions for existence...
Neural networks with piecewise constant argument and impact activation
Yılmaz, Enes; Akhmet, Marat; Department of Scientific Computing (2011)
This dissertation addresses the new models in mathematical neuroscience: artificial neural networks, which have many similarities with the structure of human brain and the functions of cells by electronic circuits. The networks have been investigated due to their extensive applications in classification of patterns, associative memories, image processing, artificial intelligence, signal processing and optimization problems. These applications depend crucially on the dynamical behaviors of the networks. In t...
An experimental study on Power Amplifier linearisation by artificial neural networks Yapay Sinir Aǧlari ile Güç Yükselteç Doǧrusalląstirma Amaçli Deneysel Bir Çalisma
Yesil, Soner; Kolagasioglu, Ahmet Ertugrul; Yılmaz, Ali Özgür (2018-07-05)
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Citation Formats
G. Top, “Almost periodic solutions of recurrently structured impulsive neural networks,” Ph.D. - Doctoral Program, Middle East Technical University, 2022.