Piecewise Linear Dynamical Systems: From Nodes to Networks

Piecewise linear (PWL) modelling has many useful applications in the applied sciences. Although the number of techniques for analysing nonsmooth systems has grown in recent years, this has typically focused on low dimensional systems and relatively little attention has been paid to networks. We aim to redress this balance with a focus on synchronous oscillatory network states. For networks with smooth nodal components, weak coupling theory, phase-amplitude reductions, and the master stability function are standard methodologies to assess the stability of the synchronous state. However, when network elements have some degree of nonsmoothness, these tools cannot be directly used and a more careful treatment is required. The work in this thesis addresses this challenge and shows how the use of saltation operators allows for an appropriate treatment of networks of PWL oscillators. This is used to augment all the aforementioned methods. The power of this formalism is illustrated by application to network problems ranging from mechanics to neuroscience

Piecewise Linear Dynamical Systems: From Nodes to Networks

Piecewise linear (PWL) modelling has many useful applications in the applied sciences. Although the number of techniques for analysing nonsmooth systems has grown in recent years, this has typically focused on low dimensional systems and relatively little attention has been paid to networks. We aim to redress this balance with a focus on synchronous oscillatory network states. For networks with smooth nodal components, weak coupling theory, phase-amplitude reductions, and the master stability function are standard methodologies to assess the stability of the synchronous state. However, when network elements have some degree of nonsmoothness, these tools cannot be directly used and a more careful treatment is required. The work in this thesis addresses this challenge and shows how the use of saltation operators allows for an appropriate treatment of networks of PWL oscillators. This is used to augment all the aforementioned methods. The power of this formalism is illustrated by application to network problems ranging from mechanics to neuroscience

Understanding the effect of white matter delays on large scale brain synchrony

The presence of myelin is a powerful structural factor that controls the conduction speed of mammalian axons. It is the combination of local synaptic activity and non-local delayed axonal interactions within the cortex that is believed to be the major source of large-scale brain signals that can be readily observed with modern neuroimaging modalities. Here, we present perspectives from neural mass and network modelling and develop a new set of mathematical tools able to unravel the contributions of space-dependent axonal delays to large-scale spatiotemporal patterning of brain activity. We first analyse a single neuronal population Wilson–Cowan neural mass model with self-feedback and a single delay and show how to construct periodic orbits for a Heaviside firing rate. For this nonsmooth model we perform linear stability analysis by augmenting Floquet theory with saltation operations. Building on this example, we then show how to treat the synchronous oscillatory state in networks of nonsmooth neural masses with multiple and heterogeneous delays. Theoretical predictions for the parameter variations that lead to instabilities of the synchronous network state and the excitation of structured spatio-temporal activity patterns are confirmed with direct numerical simulations

Yapay sinir ağlarının karmaşık dinamik davranışları

Bu projede yapay sinir ağlarının (Hopfield sinir ağları, Cohen-Grossberg sinir ağları ve shunting inhibitory hücresel sinir ağları, BAM sinir ağları) karmaşık dinamik davranışlarını inceleyeceğiz. Araştırmamız iki kısımdan oluşmaktadır: 1. Süreksizlik içeren sinir ağlarının periodik çözümlerinin varlığı, robust kararlılığı ve üstel kararlığını coincide derece teorisi, topolojik derece teorisi, Lyapunov fonksiyonelleri metodu ve lineer matris eşitsizlikleri yardımı ile inceleyeceğiz. Ayrıca bu tipteki ağlarda kaosun varlığını araştıracağız.2. Reaksiyon difüzyon terimi içeren sinir ağlarının dinamik davranışlarını inceleyeceğiz. Sabit noktanın varlığı ve tekliği ile ilgili yeni yeterli koşullar araştıracağız. Bu sinir ağlarının sabit noktalarının topolojik derece teorisi ve Lyapunov fonksiyonelleri metodu yardımı ile üstel robust kararlılıklarını inceleyeceğiz.Son olarak yukarıda bulduğumuz sonuçları örneklendirip, numerik simulasyonlarını yapacağız

On channel estimation in DC biased optical OFDM systems over VLC channels

International Conference on Advanced Technologies for Communications (ATC) -- OCT 12-14, 2016 -- Vietnam Natl Univ Univ Engn & Technol, Hanoi, VIETNAMPanayirci, Erdal/0000-0001-7328-6626WOS: 000392249400028Visible Light Communication(VLC) has been considered as a potential access option for 5G wireless systems to solve performance limitation due to bandwidth shortage at radio frequency (RF) band. in (VLC) system, illumination infrastructure has dual usage at the same time namely illumination and wireless data transmission. DC Biased optical (DCO)-OFDM has been proposed for VLC systems to provide optically power efficient solution and easy implementation. Wireless communication systems generally require estimating and tracking the fading channel in order to detect transmitted data coherently. in this work, comb type pilot arrangement with interpolation and block type pilot arrangement are proposed for the DCO-OFDM systems over visible light channels. Simulation results have verified that the proposed block type pilot arrangement based channel estimation has clear BER performance advantages compared with comb type pilot arrangement based channel estimation.IEEE, IEEE Commun Soc, Radio Elect Assoc Vietnam, Natl Instruments, Inst Elect Informat & Commun Engineers Vietnam, Natl Fdn Sci & Technol Dev, ARC, HUMAX, DHQGHN, DAIHOC CONGNGHEEuropean COST and Turkish Scientific and Research Council (TUBITAK) [110307]This work was supported by the European COST and Turkish Scientific and Research Council (TUBITAK) under Grant 110307