Browsing by Author "Eroğlu, Deniz"

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Citation Count: 3
Collective dynamics of random Janus oscillator networks
(AMER PHYSICAL SOC, 2020) Eroğlu, Deniz; Eroğlu, Deniz; Rodrigues, Francisco A.; Moreno, Yamir
Janus oscillators have been recently introduced as a remarkably simple phase oscillator model that exhibits nontrivial dynamical patterns-such as chimeras, explosive transitions, and asymmetry-induced synchronization-that were once observed only in specifically tailored models. Here we study ensembles of Janus oscillators coupled on large homogeneous and heterogeneous networks. By virtue of the Ott-Antonsen reduction scheme, we find that the rich dynamics of Janus oscillators persists in the thermodynamic limit of random regular, Erdos-Renyi, and scale-free random networks. We uncover for all these networks the coexistence between partially synchronized states and a multitude of solutions of a collective state we denominate as a breathing standing wave, which displays global oscillations. Furthermore, abrupt transitions of the global and local order parameters are observed for all topologies considered. Interestingly, only for scale-free networks, it is found that states displaying global oscillations vanish in the thermodynamic limit.
Citation Count: 0
Cycle-Star Motifs: Network Response to Link Modifications
(Springer, 2024) Eroğlu, Deniz; Kiran, Narcicegi; Eroglu, Deniz; Pereira, Tiago
Understanding efficient modifications to improve network functionality is a fundamental problem of scientific and industrial interest. We study the response of network dynamics against link modifications on a weakly connected directed graph consisting of two strongly connected components: an undirected star and an undirected cycle. We assume that there are directed edges starting from the cycle and ending at the star (master-slave formalism). We modify the graph by adding directed edges of arbitrarily large weights starting from the star and ending at the cycle (opposite direction of the cutset). We provide criteria (based on the sizes of the star and cycle, the coupling structure, and the weights of cutset and modification edges) that determine how the modification affects the spectral gap of the Laplacian matrix. We apply our approach to understand the modifications that either enhance or hinder synchronization in networks of chaotic Lorenz systems as well as R & ouml;ssler. Our results show that the hindrance of collective dynamics due to link additions is not atypical as previously anticipated by modification analysis and thus allows for better control of collective properties.
The effect of link modifications on network synchronization
(Kadir Has Üniversitesi, 2022) KIRAN, NARÇİÇEĞİ; Eroğlu, Deniz; Eroglu, Deniz
A major issue in studying complex network systems, such as neuroscience and power grids, is understanding the response of network dynamics to link modifications. The notion of network G(G, f, H) refers to di↵usively coupled identical oscillators, where isolated dynamics are chosen to be chaotic. As a consequence of the di↵usive nature, a globally synchronized state emerges as an invariant synchronization subspace, and it will be locally stable above critical coupling strength. Furthermore, the real part of the second minimum eigenvalue of the Laplacian matrix is inverse proportional to the critical coupling strength. Thus, we can use it to determine the synchronizability between two networks. Due to the asymmetry of the Laplacian matrix of a directed graph, adding directed links might cause a decrease in the real part of the second minimum eigenvalue of the Laplacian. If, after adding a link to a graph in a given network, the real part of the second minimum eigenvalue of the Laplacian matrix increases, it is called the enhancement of synchronization. Otherwise, it is called the hindrance of synchronization. In this research, we explore how the stability of synchronization at di↵usively coupled oscillators is a↵ected by link modifications for the networks created using particular motifs, i.e., cycle and star motifs. We consider a weakly connected directed graph consisting of two strongly connected components connected by directed link(s) (called cutset). We study the synchronization transitions in such networks when new directed link(s) between the components, in the opposite direction of the cutset, is added and strongly connects the whole network. We explore which properties of underlying graphs and their connected components may hinder or enhance the synchronization.
Citation Count: 10
Emergent hypernetworks in weakly coupled oscillators
(Nature Portfolio, 2022) Eroğlu, Deniz; Ocampo-Espindola, Jorge Luis; Eroglu, Deniz; Kiss, Istvan Z.; Pereira, Tiago
Networks of weakly coupled oscillators had a profound impact on our understanding of complex systems. Studies on model reconstruction from data have shown prevalent contributions from hypernetworks with triplet and higher interactions among oscillators, in spite that such models were originally defined as oscillator networks with pairwise interactions. Here, we show that hypernetworks can spontaneously emerge even in the presence of pairwise albeit nonlinear coupling given certain triplet frequency resonance conditions. The results are demonstrated in experiments with electrochemical oscillators and in simulations with integrate-and-fire neurons. By developing a comprehensive theory, we uncover the mechanism for emergent hypernetworks by identifying appearing and forbidden frequency resonant conditions. Furthermore, it is shown that microscopic linear (difference) coupling among units results in coupled mean fields, which have sufficient nonlinearity to facilitate hypernetworks. Our findings shed light on the apparent abundance of hypernetworks and provide a constructive way to predict and engineer their emergence.
Citation Count: 2
First-principle validation of Fourier's law in d=1, 2, 3 classical systems
(Elsevier, 2023) Eroğlu, Deniz; Lima, Henrique Santos; Tirnakli, Ugur; Eroglu, Deniz
We numerically study the thermal transport in the classical inertial nearest-neighbor XY ferromagnet in d = 1, 2, 3, the total number of sites being given by N = Ld, where L is the linear size of the system. For the thermal conductance sigma, we obtain sigma(T, L)L delta(d)= A(d) e-B(d) [L gamma (d)T ]eta(d) (with ez q(d) q equivalent to [1+(1-q)z]1/(1-q); ez1 = ez; A(d) > 0; B(d) > 0; q(d) > 1; eta(d) > 2; delta >= 0; gamma(d) > 0), for all values of L gamma(d)T for d = 1, 2, 3. In the L -> infinity limit, we have sigma proportional to 1/L rho sigma(d) with rho sigma(d) = delta(d)+gamma(d)eta(d)/[q(d)-1]. The material conductivity is given by kappa = sigma Ld proportional to 1/L rho kappa(d) (L -> infinity) with rho kappa(d) = rho sigma(d) - d. Our numerical results are consistent with 'conspiratory' d-dependences of (q, eta, delta, gamma), which comply with normal thermal conductivity (Fourier law) for all dimensions.(c) 2023 Published by Elsevier B.V.
Generalized synchronization: Master-slave relationship in three coupled systems
(Kadir Has Üniversitesi, 2022) Doğan, Gizem; Eroğlu, Deniz; Eroglu, Deniz
Synchronization is an important phenomenon for complex, biological, and physical systems such as the brain, i.e., Parkinson’s disease, heart beating, hand-clapping, power grids, lasers, and many others. Intuitively, we can express synchronization as strong correlations between coupled systems. We can state two scenarios in this manner. One is synchronization between identical systems, which is called complete synchronization; the other is the synchronization between the non-identical systems, called generalized synchronization. In this thesis, initially, we considered the two coupled systems and calculated the critical coupling value for the generalized synchronization analytically. More precisely, the Lorenz system drives two R¨ossler systems. We investigated the critical coupling value for synchronization numerically. However, real-world examples are much more complex. The most straightforward case was the two coupled systems for the generalized synchronization, and next, we focus on three coupled systems. In particular, suppose that we have three coupled one Lorenz and two R¨ossler systems. In our example, the Lorenz system drives the first R¨ossler system, and first R¨ossler system drives the second R¨ossler system, and finally, the second R¨ossler system also drives the Lorenz system. We calculated the critical coupling of the whole system for generalized synchronization and analyzed the time series for each system.
Citation Count: 10
Holocene climate forcings and lacustrine regime shifts in the Indian summer monsoon realm
(Wıley, 2020) Eroğlu, Deniz; Marwan, Norbert; Eroğlu, Deniz; Goswami, Bedartha; Mishra, Praveen Kuma; Gaye, Birgit; Anoop, Akhil; Stebich, Martina; Jehangir, Arshid; Basavaiah, Nathani
Extreme climate events have been identified both in meteorological and long-term proxy records from the Indian summer monsoon (ISM) realm. However, the potential of palaeoclimate data for understanding mechanisms triggering climate extremes over long time scales has not been fully exploited. A distinction between proxies indicating climate change, environment, and ecosystem shift is crucial for enabling a comparison with forcing mechanisms (e.g. El-Nino Southern Oscillation). In this study we decouple these factors using data analysis techniques [multiplex recurrence network (MRN) and principal component analyses (PCA)] on multiproxy data from two lakes located in different climate regions - Lonar Lake (ISM dominated) and the high-altitude Tso Moriri Lake (ISM and westerlies influenced). Our results indicate that (i) MRN analysis, an indicator of changing environmental conditions, is associated with droughts in regions with a single climate driver but provides ambiguous results in regions with multiple climate/environmental drivers; (ii) the lacustrine ecosystem was 'less sensitive' to forcings during the early Holocene wetter periods; (iii) archives in climate zones with a single climate driver were most sensitive to regime shifts; (iv) data analyses are successful in identifying the timing of onset of climate change, and distinguishing between extrinsic and intrinsic (lacustrine) regime shifts by comparison with forcing mechanisms. Our results enable development of conceptual models to explain links between forcings and regional climate change that can be tested in climate models to provide an improved understanding of the ISM dynamics and their impact on ecosystems. (c) 2020 John Wiley & Sons, Ltd.
Citation Count: 17
Multifaceted Dynamics of Janus Oscillator Networks
(Amer Physical Soc., 2019) Eroğlu, Deniz; Eroğlu, Deniz; Motter, Adilson E.
Recent research has led to the discovery of fundamental new phenomena in network synchronization including chimera states explosive synchronization and asymmetry-induced synchronization. Each of these phenomena has thus far been observed only in systems designed to exhibit that one phenomenon which raises the questions of whether they are mutually compatible and if so under what conditions they co-occur. Here we introduce a class of remarkably simple oscillator networks that concurrently exhibit all of these phenomena. The dynamical units consist of pairs of nonidentical phase oscillators which we refer to as Janus oscillators by analogy with Janus particles and the mythological figure from which their name is derived. In contrast to previous studies these networks exhibit (i) explosive synchronization with identical oscillators, (ii) extreme multistability of chimera states including traveling intermittent and bouncing chimeras, and (iii) asymmetry-induced synchronization in which synchronization is promoted by random oscillator heterogeneity. These networks also exhibit the previously unobserved possibility of inverted synchronization transitions in which a transition to a more synchronous state is induced by a reduction rather than an increase in the coupling strength. These various phenomena are shown to emerge under rather parsimonious conditions and even in locally connected ring topologies which has the potential to facilitate their use to control and manipulate synchronization in experiments.
Citation Count: 0
Network dynamics reconstruction from data
(Scıentıfıc Technıcal Research Councıl Turkey-Tubıtak, 2020) Eroğlu, Deniz
We consider the problem of recovering the model of a complex network of interacting dynamical units from time series of observations. We focus on typical networks which exhibit heterogeneous degrees, i.e. where the number of connections varies widely across the network, and the coupling strength for a single interaction is small. In these networks, the behavior of each unit varies according to their connectivity. Under these mild assumptions, our method provides an effective network reconstruction of the network dynamics. The method is robust to a certain size of noise and only requires relatively short time series on the state variable of most nodes to determine: how well-connected a particular node is, the distribution of the nodes' degrees in the network, and the underlying dynamics.
Citation Count: 9
Network structural origin of instabilities in large complex systems
(Amer Assoc Advancement Science, 2022) Eroğlu, Deniz; Nishikawa, Takashi; Eroglu, Deniz; Motter, Adilson E.
A central issue in the study of large complex network systems, such as power grids, financial networks, and ecological systems, is to understand their response to dynamical perturbations. Recent studies recognize that many real networks show nonnormality and that nonnormality can give rise to reactivity-the capacity of a linearly stable system to amplify its response to perturbations, oftentimes exciting nonlinear instabilities. Here, we identify network structural properties underlying the pervasiveness of nonnormality and reactivity in real directed networks, which we establish using the most extensive dataset of such networks studied in this context to date. The identified properties are imbalances between incoming and outgoing network links and paths at each node. On the basis of this characterization, we develop a theory that quantitatively predicts nonnormality and reactivity and explains the observed pervasiveness. We suggest that these results can be used to design, upgrade, control, and manage networks to avoid or promote network instabilities.
Citation Count: 13
Nonlinear time series analysis of palaeoclimate proxy records
(Pergamon-Elsevier Science Ltd, 2021) Eroğlu, Deniz; Donges, Jonathan F.; Donner, Reik, V; Eroglu, Deniz
Identifying and characterising dynamical regime shifts, critical transitions or potential tipping points in palaeoclimate time series is relevant for improving the understanding of often highly nonlinear Earth system dynamics. Beyond linear changes in time series properties such as mean, variance, or trend, these nonlinear regime shifts can manifest as changes in signal predictability, regularity, complexity, or higher-order stochastic properties such as multi-stability. In recent years, several classes of methods have been put forward to study these critical transitions in time series data that are based on concepts from nonlinear dynamics, complex systems science, information theory, and stochastic analysis. These include approaches such as phase space-based recurrence plots and recurrence networks, visibility graphs, order pattern-based entropies, and stochastic modelling. Here, we review and compare in detail several prominent methods from these fields by applying them to the same set of marine palaeoclimate proxy records of African climate variations during the past 5 million years. Applying these methods, we observe notable nonlinear transitions in palaeoclimate dynamics in these marine proxy records and discuss them in the context of important climate events and regimes such as phases of intensified Walker circulation, marine isotope stage M2, the onset of northern hemisphere glaciation and the mid-Pleistocene transition. We find that the studied approaches complement each other by allowing us to point out distinct aspects of dynamical regime shifts in palaeoclimate time series. We also detect significant correlations of these nonlinear regime shift indicators with variations of Earth's orbit, suggesting the latter as potential triggers of nonlinear transitions in palaeoclimate. Overall, the presented study underlines the potentials of nonlinear time series analysis approaches to provide complementary information on dynamical regime shifts in palaeoclimate and their driving processes that cannot be revealed by linear statistics or eyeball inspection of the data alone. (C) 2021 The Authors. Published by Elsevier Ltd.
Citation Count: 3
Reconstructing Network Dynamics of Coupled Discrete Chaotic Units from Data
(Amer Physical Soc, 2023) Eroğlu, Deniz; Eroglu, Deniz
Reconstructing network dynamics from data is crucial for predicting the changes in the dynamics of complex systems such as neuron networks; however, previous research has shown that the reconstruction is possible under strong constraints such as the need for lengthy data or small system size. Here, we present a recovery scheme blending theoretical model reduction and sparse recovery to identify the governing equations and the interactions of weakly coupled chaotic maps on complex networks, easing unrealistic constraints for real-world applications. Learning dynamics and connectivity lead to detecting critical transitions for parameter changes. We apply our technique to realistic neuronal systems with and without noise on a real mouse neocortex and artificial networks.
Citation Count: 13
Recurrence analysis of extreme event-like data
(COPERNICUS GESELLSCHAFT MBH, 2021) Eroğlu, Deniz; Goswami, Bedartha; Hirata, Yoshito; Eroğlu, Deniz; Merz, Bruno; Kurths, Juergen; Marwan, Norbert
The identification of recurrences at various time-scales in extreme event-like time series is challenging because of the rare occurrence of events which are separated by large temporal gaps. Most of the existing time series analysis techniques cannot be used to analyze an extreme event-like time series in its unaltered form. The study of the system dynamics by reconstruction of the phase space using the standard delay embedding method is not directly applicable to event-like time series as it assumes a Euclidean notion of distance between states in the phase space. The edit distance method is a novel approach that uses the point-process nature of events. We propose a modification of edit distance to analyze the dynamics of extreme event-like time series by incorporating a nonlinear function which takes into account the sparse distribution of extreme events and utilizes the physical significance of their temporal pattern. We apply the modified edit distance method to event-like data generated from point process as well as flood event series constructed from discharge data of the Mississippi River in the USA and compute their recurrence plots. From the recurrence analysis, we are able to quantify the deterministic properties of extreme event-like data. We also show that there is a significant serial dependency in the flood time series by using the random shuffle surrogate method.
Citation Count: 14
Revealing Dynamics, Communities, and Criticality from Data
(Amer Physical Soc, 2020) Eroğlu, Deniz; Tanzi, Matteo; van Strien, Sebastian; Pereira, Tiago
Complex systems such as ecological communities and neuron networks are essential parts of our everyday lives. These systems are composed of units which interact through intricate networks. The ability to predict sudden changes in the dynamics of these networks, known as critical transitions, from data is important to avert disastrous consequences of major disruptions. Predicting such changes is a major challenge as it requires forecasting the behavior for parameter ranges for which no data on the system are available. We address this issue for networks with weak individual interactions and chaotic local dynamics. We do this by building a model network, termed an effective network, consisting of the underlying local dynamics and a statistical description of their interactions. We show that behavior of such networks can be decomposed in terms of an emergent deterministic component and a fluctuation term. Traditionally, such fluctuations are filtered out. However, as we show, they are key to accessing the interaction structure. We illustrate this approach on synthetic time series of realistic neuronal interaction networks of the cat cerebral cortex and on experimental multivariate data of optoelectronic oscillators. We reconstruct the community structure by analyzing the stochastic fluctuations generated by the network and predict critical transitions for coupling parameters outside the observed range.
Citation Count: 6
Sampling rate-corrected analysis of irregularly sampled time series
(Amer Physical Soc, 2022) Eroğlu, Deniz; Fernandez, Cinthya N.; Eroglu, Deniz; Hartland, Adam; Breitenbach, Sebastian F. M.; Marwan, Norbert
The analysis of irregularly sampled time series remains a challenging task requiring methods that account for continuous and abrupt changes of sampling resolution without introducing additional biases. The edit distance is an effective metric to quantitatively compare time series segments of unequal length by computing the cost of transforming one segment into the other. We show that transformation costs generally exhibit a nontrivial relationship with local sampling rate. If the sampling resolution undergoes strong variations, this effect impedes unbiased comparison between different time episodes. We study the impact of this effect on recurrence quantification analysis, a framework that is well suited for identifying regime shifts in nonlinear time series. A constrained randomization approach is put forward to correct for the biased recurrence quantification measures. This strategy involves the generation of a type of time series and time axis surrogates which we call sampling-rate-constrained (SRC) surrogates. We demonstrate the effectiveness of the proposed approach with a synthetic example and an irregularly sampled speleothem proxy record from Niue island in the central tropical Pacific. Application of the proposed correction scheme identifies a spurious transition that is solely imposed by an abrupt shift in sampling rate and uncovers periods of reduced seasonal rainfall predictability associated with enhanced El Nino-Southern Oscillation and tropical cyclone activity.
Citation Count: 5
Transformation cost spectrum for irregularly sampled time series
(Springer Heidelberg, 2023) Eroğlu, Deniz; Eroglu, Deniz
Irregularly sampled time series analysis is a common problem in various disciplines. Since conventional methods are not directly applicable to irregularly sampled time series, a common interpolation approach is used; however, this causes data distortion and consequently biases further analyses. We propose a method that yields a regularly sampled time series spectrum of costs with minimum information loss. Each time series in this spectrum is a stationary series and acts as a difference filter. The transformation costs approach derives the differences between consecutive and arbitrarily sized segments. After obtaining regular sampling, recurrence plot analysis is performed to distinguish regime transitions. The approach is applied to a prototypical model to validate its performance and to different palaeoclimate proxy data sets located around Africa to identify critical climate transition periods during the last 5 million years and their characteristic properties.