Stabilnost BAM neuronske mreže

master's thesis

• Title (english): Stability of BAM neural network
• Author: Petra Vidović
• Mentor: Vesna Županović (mentor)
• Committee member: Vesna Županović (predsjednik povjerenstva)
• Committee member: Dragan Jevtić (član povjerenstva)
• Committee member: Marin Vuković (član povjerenstva)
• Granter: University of Zagreb; Faculty of Electrical Engineering and Computing; Zagreb
• Defense date and country: 2014-07-09, Croatia
• Scientific / art field, discipline and subdiscipline: TECHNICAL SCIENCES; Computing
• Scientific / art field, discipline and subdiscipline: TECHNICAL SCIENCES; Electrical Engineering

Abstract

Neuronske mreže su sustavi modelirani od procesirajućih elemenata neurona po uzoru na mrežu ljudskih moždanih stanica. Mreža ima specifičnu strukturu obrade informacija sastavljene od velikog broja međusobno povezanih neurona koji zajednički rade na rješavanju određenog problema. Neuronska mreža s dvosmjernom asocijativnom memorijom (engl. Bidirectional Associative Memory - BAM) ima sposobnost izravno adresirati sadržaj. U radu je prikazana BAM neuronska mreža s tri neurona te je modelirana sustavom diferencijalnih jednadžbi s kašnjenjem. Takav model pojavio se po uzoru na Hopfieldovu neuronsku mrežu potaknut idejom da kod prijenosa signala dolazi do kašnjenja. Primjenom teorije, a zatim i numeričke simulacije, ispitana je stabilnost pojednostavljene BAM neuronske mreže te su istraženi uvjeti pod kojima sustav gubi stabilnost te dolazi do pojave Hopfove bifurkacije.

Abstract (english)

Neural networks are modeled by the processing elements of neurons based on a network of human brain cells. The network has a specific structure of the information processing composed of many interconnected neurons that work together to solve a particular problem. Neural network with bidirectional associative memory (BAM) has the ability to directly address the content. This work presents the BAM neural network with three neurons and it is modeled by a system of differential equations with delays. Such model has appeared by the model of Hopfield neural network driven by the idea that signal transmission has delays. By applying the theory, and then the numerical simulations, the stability of a simplified BAM neural network is examined, and the conditions under which the system loses stability, and suffers from the Hopf bifurcation is explored.

• Keywords: neuronska mreža; dvosmjerna asocijativna memorija; stabilnost; Hopfova bifurkacija; diferencijalne jednadžbe s kašnjenjem
• Keywords (english): neural network; bidirectional associative memory; stability; Hopf bifurcation; differential equations with delay
• Language: croatian
• URN:NBN: urn:nbn:hr:168:815200
• Study programme: Title: Information and Communication Technology; Study programme type: university; Study level: graduate; Academic / professional title: magistar/magistra inženjer/inženjerka informacijske i komunikacijske tehnologije (magistar/magistra inženjer/inženjerka informacijske i komunikacijske tehnologije)
• Type of resource: Text
• File origin: Born digital
• Access conditions: Closed access
• Created on: 2018-02-06 14:19:19