Analiza dinamike grupe Hindmarsh-Rose neurona s usmjerenim vezama

master's thesis

• Title (english): Analysis of a group of Hindmarsh-Rose neurons with directional connections
• Author: Noah Marko Mesić
• Mentor: Vesna Županović (mentor)
• Committee member: Vesna Županović (predsjednik povjerenstva)
• Committee member: Dario Bojanjac (član povjerenstva)
• Committee member: Brigita Ferčec (član povjerenstva); ISVU oznaka: BF040
• Granter: University of Zagreb; Faculty of Electrical Engineering and Computing; Zagreb
• Defense date and country: 2024-09-13, Croatia

Abstract

Dinamički sustav dva identična Hindmarsh-Rose neurona povezana dvosmjernom vezom
simuliran je u programu MatCont. Sustav je analiziran ovisno o bifurkacijskom parametru I
koji predstavlja struju na ulazu u neurone. Pokazano je postojanje sinkronizacijske mnogostrukosti u faznom prostoru kad se sinkronizirani neuroni ponašaju kao da veza između njih ne postoji. Jedna singularna točka postoji na toj mnogostrukosti čija stabilnost ovisi o bifurkacijskom parametru. Identificirane su vrijednosti parametra za koje dolazi do Andronov-Hopf
bifurkacije te je promatrano ponašanje nastalih graničnih ciklusa. Ljapunovljevi eksponenti,
izračunati programom Lyapunov Exponents Toolbox u MATLAB-u, korišteni su za detektiranje
kaotičnog ponašanja koje je karakteristično za Hindmarsh-Rose neuron.

Abstract (english)

A dynamical system of two coupled identical Hindmarsh-Rose neurons was simulated in
MatCont. The resulting system was analyzed depending on the bifurcation parameter I,
which represents the input current to the neurons. The existence of a synchronization manifold
in the phase space was demonstrated, where the synchronized neurons behave as if
the connection between them does not exist. There is a single fixed point in this manifold
whose stability depends on the bifurcation parameter. The values of the parameter at which
Andronov-Hopf bifurcation occurs were identified, and the behavior of the resulting limit
cycles was observed. Lyapunov exponents calculated using Lyapunov Exponents Toolbox
in MATLAB were used to detect chaotic behavior, which is characteristic of the Hindmarsh-
Rose neuron.

• Keywords: dinamički sustavi; neuroni povezani usmjerenim vezama; Hindmarsh-Rose; bifurkacije
• Keywords (english): dynamic systems; coupled neurons; Hindmarsh-Rose; bifurcations
• Language: croatian
• URN:NBN: urn:nbn:hr:168:447137
• Study programme: Title: Computing; Study programme type: university; Study level: graduate; Academic / professional title: magistar/magistra inženjer/inženjerka računarstva (magistar/magistra inženjer/inženjerka računarstva)
• Type of resource: Text
• File origin: Born digital
• Access conditions: Closed access
• Created on: 2024-10-12 21:33:46