20.500.12556/DKUM-85851 Dinamična robustnost in prehod v staranje v omrežjih sklopljenih oscilatorjev magistrsko delo Dynamical robustness and aging transitions in networks of coupled oscillators Biološka omrežja so v splošnem odporna na okvare posameznih enot, toda v vsakem omrežju obstaja prelomna točka, pri kateri se sposobnost delovanja poslabša do neuporabnosti. To se lahko kaže kot bolezen ali izguba funkcije, kar je pogosto težko odpraviti. Iz tega razloga je pomembno preučevati pojave takih kolektivnih okvar, ki sledijo postopni disfunkciji posameznih gradnikov, da bi lahko sprejeli ukrepe za njihovo preprečitev. Na področju dinamičnih sistemov se tovrstni prehodi imenujejo prehod v staranje (ang. aging transition). Temu pojavu se posvetimo tudi v tej magistrski nalogi in najprej prikažemo koncept prehoda v staranje v omrežjih globalno sklopljenih in homogenih oscilatorjev z limitnim ciklom, pri katerih dinamiko posameznih oscilatorjev določa Poincaréjev oscilator. Pokažemo, da se prehodi v staranje v takih omrežjih obnašajo dokaj predvidljivo ter da imata jakost sklopitve in oddaljenost od točke bifurkacije monotono vlogo pri dinamični robustnosti sistema. Nato se osredotočimo na preučevanje kolektivnih okvar v biološko bolj realističnih omrežjih, ki sestojijo iz povezanih ekscitabilnih enot, interakcije med njimi pa izkazujejo lastnosti kompleksnega omrežja. Le-to je heterogeno in ima visoko modularnost in lastnosti mrež malega sveta. Dinamiko posameznih ekscitabilnih elementov določa paradigmatski model FitzHugh-Nagumo, ki se pogosto uporablja za simulacije dinamike električno ekscitabilnih celic. Kot dejavnike za kolektivno odpoved obravnavamo jakost sklopitve, razdaljo od točke bifurkacije in poleg tega še različne strategije staranja. Ugotovimo, da pri srednjih jakostih sklopitve omrežje ostane globalno aktivno najdlje, kadar se v omrežju najprej deaktivirajo vozli z velikim številom povezav. To se dobro ujema s predhodno objavljenimi rezultati. Ti so pokazali, da so lahko, predvsem pri šibki sklopitvi, omrežja oscilatorjev zelo občutljiva na ciljno deaktivacijo vozlov z majhnim številom povezav. Toda naše podrobne analize pokažejo, da najučinkovitejša strategija za doseganje kolektivne odpovedi ni le nemonotono odvisna od jakosti sklopitve, temveč je odvisna od sovisnega vpliva jakosti sklopitve in oddaljenosti točke bifurkacije, ki kroji raven stabilnosti oscilatornega režima. V magistrski nalogi tako podamo celovit opis dejavnikov kolektivne odpovedi v ekscitabilnih omrežjih, kar vodi do globljega razumevanja okvar v takih sistemih. Biological networks are remarkably robust to failures of its individual units. But each network still has a breaking point at which its collective function deteriorates to uselessness. This may manifest as a disease or loss of function that is often difficult to reverse. It is therefore important to determine when such collective failures occur in order to enact measures to avoid them. In the field of dynamical systems, such transitions are referred to as aging transitions. In this master thesis we address this phenomenon by firstly showing the concepts of aging transition in networks of globally coupled and homogeneous limit cycle oscillators, where the dynamics of the individual oscillator is determined by the Poincaré oscillator. We show that aging transitions in such networks behave quite predictably, and that the coupling strength and the distance from the bifurcation point play a monotonic role in the dynamical robustness of the system. Next, we shift our focus to the study of collective failures in more biologically realistic networks, which consist of connected excitable units, where the interactions between them exhibit the properties of a complex network. These networks are heterogeneous, with high modularity and small-world properties. The dynamics of the individual excitable elements is determined by the paradigmatic FitzHugh-Nagumo model, which is widely used for simulations of the dynamics of electrically excitable cells. We consider coupling strengths, bifurcation distances and in addition various aging scenarios as potential culprits of collective failure. We find that for intermediate coupling strengths the network remains globally active the longest if the high-degree nodes are the first targets of deactivation. This agrees well with previously published results, which showed that oscillatory networks can be highly fragile to the targeted inactivation of low-degree nodes, especially under weak coupling. However, our detailed analyses shows that the most effective strategy to achieve collective failure is not only non-monotonically dependent on the coupling strength, but also depends on the interplay between the coupling strength and the distance of the bifurcation point, which tailors the level of stability of the oscillatory regime. In this thesis, we thus provide a comprehensive account of determinants of collective failure in excitable networks, leading to a deeper understanding of failures in such systems. prehod v staranje oscilatorji z limitnim ciklom ekscitabilni oscilatorji kompleksno omrežje bifurkacija globalna aktivnost. aging transition limit cycle oscillators excitable oscillators networks complex networks bifurcation global activity. true true false [U. Barać] Slovenski jezik Angleški jezik Magistrsko delo/naloga 2023-09-14 20:29:44 2023-09-28 14:35:44 2023-09-29 03:06:03 0000-00-00 00:00:00 2023 0 Maribor 0 Maribor 34 f. 0000-00-00 NiDoloceno NiDoloceno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 621.373.1(043.2) 166231043 MAG_Barac_Uros_2023.pdf MAG_Barac_Uros_2023.pdf 1 C805AE593457DB25D4863B03EAC5EB2C 13694ce2ae47a9e91fdb0843ce7fd68202a139ab4744146b8ec5a73f7f38f301 0b682e3a-532e-11ee-a747-00155d000105 https://dk.um.si/Dokument.php?lang=slv&id=172258 Fakulteta za naravoslovje in matematiko 0 0 0