Stability analysis of neural networks with piecewise constant argument

Karacaören, Meltem
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. 


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...
Position estimation for timing belt drives of precision machinery using structured neural networks
KILIÇ, Ergin; DOĞRUER, CAN ULAŞ; Dölen, Melik; Koku, Ahmet Buğra (2012-05-01)
This paper focuses on a viable position estimation scheme for timing-belt drives using artificial neural networks. In this study, the position of a carriage (load) is calculated via a structured neural network topology accepting input from a position sensor on the actuator side of the timing belt. The paper presents a detailed discussion on the source of transmission errors. The characteristics of the error in different operation regimes are exploited to construct different network topologies. That is, a re...
Citation Formats
M. Karacaören, “Stability analysis of neural networks with piecewise constant argument,” Ph.D. - Doctoral Program, Middle East Technical University, 2017.