Show/Hide Menu
Hide/Show Apps
Logout
Türkçe
Türkçe
Search
Search
Login
Login
OpenMETU
OpenMETU
About
About
Open Science Policy
Open Science Policy
Open Access Guideline
Open Access Guideline
Postgraduate Thesis Guideline
Postgraduate Thesis Guideline
Communities & Collections
Communities & Collections
Help
Help
Frequently Asked Questions
Frequently Asked Questions
Guides
Guides
Thesis submission
Thesis submission
MS without thesis term project submission
MS without thesis term project submission
Publication submission with DOI
Publication submission with DOI
Publication submission
Publication submission
Supporting Information
Supporting Information
General Information
General Information
Copyright, Embargo and License
Copyright, Embargo and License
Contact us
Contact us
Stability analysis of neural networks with piecewise constant argument
Download
index.pdf
Date
2017
Author
Karacaören, Meltem
Metadata
Show full item record
Item Usage Stats
309
views
113
downloads
Cite This
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.
Subject Keywords
Mathematical constants.
,
Neural networks (Computer science).
URI
http://etd.lib.metu.edu.tr/upload/12620724/index.pdf
https://hdl.handle.net/11511/26304
Collections
Graduate School of Natural and Applied Sciences, Thesis
Suggestions
OpenMETU
Core
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...
Learning Deep Temporal Representations for fMRI Brain Decoding
Firat, Orhan; Aksan, Emre; Oztekin, Ilke; Yarman Vural, Fatoş Tunay (2015-07-11)
Functional magnetic resonance imaging (fMRI) produces low number of samples in high dimensional vector spaces which is hardly adequate for brain decoding tasks. In this study, we propose a combination of autoencoding and temporal convolutional neural network architecture which aims to reduce the feature dimensionality along with improved classification performance. The proposed network learns temporal representations of voxel intensities at each layer of the network by leveraging unlabeled fMRI data with re...
Case studies on the use of neural networks in eutrophication modeling
Karul, C; Soyupak, S; Cilesiz, AF; Akbay, N; Germen, E (2000-10-30)
Artificial neural networks are becoming more and more common to be used in development of prediction models for complex systems as the theory behind them develops and the processing power of computers increase. A three layer Levenberg-Marquardt feedforward learning algorithm was used to model the eutrophication process in three water bodies of Turkey (Keban Dam Reservoir, Mogan and Eymir Lakes). Despite the very complex and peculiar nature of Keban Dam, a relatively good correlation (correlation coefficient...
Estimation of nonlinear neural source interactions via sliced bicoherence
Özkurt, Tolga Esat (2016-09-01)
Neural oscillations and their spatiotemporal interactions are of interest for the description of brain mechanisms. This study offers a novel third order spectral coupling measure named "sliced bicoherence". It is the diagonal slice of cross-bicoherence allowing an efficient quantification of the nonlinear interactions between neural sources. Our methodology comprises an indirect estimation method, a parametric confidence level formula and a subtracted version for robustness to volume conduction. The methodo...
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...
Citation Formats
IEEE
ACM
APA
CHICAGO
MLA
BibTeX
M. Karacaören, “Stability analysis of neural networks with piecewise constant argument,” Ph.D. - Doctoral Program, Middle East Technical University, 2017.