Smer sklopitve v nelinearnih sistemih : magistrsko delo

Brešar, Martin (author), Horvat, Martin (mentor), Boškoski, Pavle (comentor)

Delo obravnava dve metodi za določitev smeri sklopitve sistemov na podlagi njihovih meritev. Prva temelji na informacijski teoriji, druga pa na časovno-frekvenčni transformaciji. Cilj naloge je preizkusiti njuno uporabnost za določitev smeri sklopitve sistemov v različnih dinamičnih režimih ter za reševanje inverznega problema iskanja modelskih parametrov sklopitve. Testiramo jih na modelu sklopljenih Duffingovih oscilatorjev v kaotičnem in regularnem dinamičnem režimu. Na sistemih v regularnem režimu se problem določitve smeri sklopitve izkaže za enostavnega, rešljiv pa je tudi v kaotičnem režimu. Inverzni problem je rešljiv, razen pri sklopitvi dveh kaotičnih sistemov. Predstavimo tudi statisični test z uporabo nadomestnih signalov za potrditev obstoja sklopitve. Na koncu obravnavamo tudi aplikacijo metod v medicini kot diagnostično orodje.

• Language: Slovenian
• Keywords: sklopitev dinamičnih sistemov, nelinearna dinamika, informacijska teorija, časovno-frekvenčna transformacija, nadomestni signali
• Work type: Master's thesis/paper
• Typology: 2.09 - Master's Thesis
• Organization: FMF - Faculty of Mathematics and Physics
• Year: 2020
• PID: 20.500.12556/RUL-119597
• COBISS.SI-ID: 27600387
• Publication date in RUL: 10.09.2020

Secondary language

• Language: English
• Title: Direction of coupling in nonlinear systems

Abstract

The thesis discusses two methods for determining the direction of coupling of systems from their measurements. The first method is based on information theory and the second one on time-frequency transformation. The goal of the thesis is to test their usefulness for determining the direction of coupling of systems in different dynamic regimes and for solving the inverse problem of inferring the model parameters of coupling. We test them on the model of two coupled Duffing oscillators in a chaotic and a regular dynamic regime. For the systems in regular regime, the problem of determining the direction of coupling turns out to be simple, and it is also solvable in a chaotic regime. The inverse problem is solvable, except for the coupling of two chaotic systems. We also introduce a statistical test using surrogate data to confirm the existence of coupling. Finally, we discuss the application of the methods in medicine as a diagnostic tool.

• Keywords: coupling in dynamical systems, nonlinear dynamics, information theory, time-frequency transformation, surrogate data