Neural networks with piecewise constant argument and impact activation

Download

index.pdf

Date

2011

Author

Yılmaz, Enes

Metadata

Show full item record

Item Usage Stats

315
views

126
downloads

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 this thesis the dynamics are presented by differential equations with discontinuities: differential equations with piecewise constant argument of generalized type, and both impulses at fixed moments and piecewise constant argument. A discussion of the models, which are appropriate for the proposed applications, are also provided. Qualitative analysis of existence and uniqueness of solutions, global asymptotic stability, uniform asymptotic stability and global exponential stability of equilibria, existence of periodic solutions and their global asymptotic stability for these networks are obtained. Examples with numerical simulations are given to validate the theoretical results. All the properties are rigorously approved by using methods for differential equations with discontinuities: existence and uniqueness theorems; stability analysis through the Second Lyapunov method and linearization. It is the first time that the problem of stability with the method of Lyapunov functions for differential equations with piecewise constant argument of generalized type is investigated. Despite the fact that these equations are with deviating argument, stability criteria are merely found in terms of Lyapunov functions.

Subject Keywords

Neural networks (Computer science)

URI

http://etd.lib.metu.edu.tr/upload/12613307/index.pdf
https://hdl.handle.net/11511/21246

Collections

Graduate School of Applied Mathematics, Thesis

Suggestions

OpenMETU
Core

Stability analysis of neural networks with piecewise constant argument Karacaören, Meltem; Akhmet, Marat; Department of Mathematics (2017) 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...
Computational representation of protein sequences for homology detection and classification Oğul, Hasan; Mumcuoğlu, Ünal Erkan; Department of Information Systems (2006) Machine learning techniques have been widely used for classification problems in computational biology. They require that the input must be a collection of fixedlength feature vectors. Since proteins are of varying lengths, there is a need for a means of representing protein sequences by a fixed-number of features. This thesis introduces three novel methods for this purpose: n-peptide compositions with reduced alphabets, pairwise similarity scores by maximal unique matches, and pairwise similarity scores by...
Representing temporal knowledge in connectionist expert systems Alpaslan, Ferda Nur (1996-09-27) This paper introduces a new temporal neural networks model which can be used in connectionist expert systems. Also, a Variation of backpropagation algorithm, called the temporal feedforward backpropagation algorithm is introduced as a method for training the neural network. The algorithm was tested using training examples extracted from a medical expert system. A series of experiments were carried out using the temporal model and the temporal backpropagation algorithm. The experiments indicated that the alg...
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...
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

E. Yılmaz, “Neural networks with piecewise constant argument and impact activation,” Ph.D. - Doctoral Program, Middle East Technical University, 2011.