Almost periodic solutions of recurrently structured impulsive neural networks

Download

10460770.pdf

Date

2022-3-28

Author

Top, Gülbahar

Metadata

Show full item record

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Item Usage Stats

325
views

202
downloads

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.

Subject Keywords

Asymptotic stability, B-equivalence method, Discontinuous almost periodic motions, Neural networks with negative/positive capacitance, Recurrently structured impacts, Recurrent impulsive neural networks

URI

https://hdl.handle.net/11511/96807

Collections

Graduate School of Natural and Applied Sciences, Thesis

Suggestions

OpenMETU
Core

Almost Periodic Solutions of Recurrent Neural Networks with State-Dependent and Structured Impulses Akhmet, Marat; Erim, Gülbahar (2023-01-01) The subject of the present paper is recurrent neural networks with variable impulsive moments. The impact activation functions are specified such that the structure for the jump equations are in full accordance with that one for the differential equation. The system studied in this paper covers the works done before, not only because the impacts have recurrent form, but also impulses are not state-dependent. The conditions for existence and uniqueness of asymptotically stable discontinuous almost periodic s...
IMPULSIVE SICNNS WITH CHAOTIC POSTSYNAPTIC CURRENTS 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...
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...
Artificial-neural-network prediction of hexagonal lattice parameters for non-stoichiometric apatites Kockan, Umit; Ozturk, Fahrettin; Evis, Zafer (2014-01-01) In this study, hexagonal lattice parameters (a and c) and unit-cell volumes of non-stoichiometric apatites of M-10(TO4)(6)X-2 are predicted from their ionic radii with artificial neural networks. A multilayer-perceptron network is used for training. The results indicate that the Bayesian regularization method with four neurons in the hidden layer with a tansig activation function and one neuron in the output layer with a purelin function gives the best results. It is found that the errors for the predicted ...
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...

Citation Formats

G. Top, “Almost periodic solutions of recurrently structured impulsive neural networks,” Ph.D. - Doctoral Program, Middle East Technical University, 2022.