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Jiachen Sun, Rong Liu, Zhengping Fan, Jiarong Xie, Xiao Ma, Yanqing Hu
The network dismantling problem is one of the most fundamental problems in network science. It aims to identify the minimum number of nodes, such that after their removal the network is broken into many disconnected pieces with a sub-extensive size. However, the identification of the minimum removed nodes belongs to the class of nondeterministic polynomial problems. Although many heuristic algorithms have been proposed to identify the removed nodes, the smallest dismantling set remains unknown. Therefore, the determination of a good lower bound of dismantling sets is of great significance to evaluating the performances of heuristic algorithms...
June 2018: Chaos
André Röhm, Kathy Lüdge, Isabelle Schneider
In the model system of two instantaneously and symmetrically coupled identical Stuart-Landau oscillators, we demonstrate that there exist stable solutions with symmetry-broken amplitude- and phase-locking. These states are characterized by a non-trivial fixed phase or amplitude relationship between both oscillators, while simultaneously maintaining perfectly harmonic oscillations of the same frequency. While some of the surrounding bifurcations have been previously described, we present the first detailed analytical and numerical description of these states and present analytically and numerically how they are embedded in the bifurcation structure of the system, arising both from the in-phase and the anti-phase solutions, as well as through a saddle-node bifurcation...
June 2018: Chaos
Nastaran Lotfi, Amir Hossein Darooneh, Francisco A Rodrigues
Seismic time series has been mapped as a complex network, where a geographical region is divided into square cells that represent the nodes and connections are defined according to the sequence of earthquakes. In this paper, we map a seismic time series to a temporal network, described by a multiplex network, and characterize the evolution of the network structure in terms of the eigenvector centrality measure. We generalize previous works that considered the single layer representation of earthquake networks...
June 2018: Chaos
J Hizanidis, N Lazarides, G P Tsironis
The radio frequency (rf) Superconducting QUantum Interference Device (SQUID) is a highly nonlinear oscillator exhibiting the rich dynamical behavior. It has been studied for many years and it has found numerous applications in magnetic field sensors, in biomagnetism, in non-destructive evaluation, and gradiometers, among others. Despite its theoretical and practical importance, there is relatively very little work on its multistability, chaotic properties, and bifurcation structure. In the present work, the dynamical properties of the SQUID in the strongly nonlinear regime are demonstrated using a well-established model whose parameters lie in the experimentally accessible range of values...
June 2018: Chaos
Chatchai Wannaboon, Masayoshi Tachibana, Wimol San-Um
A full-custom design of chaos-based True Random-Bit Generator (TRBG) implemented on a 0.18-μm CMOS technology is presented with unique composition of three major components, i.e., (i) chaotic jerk oscillator, (ii) ΔΣ modulator, and (iii) simple pre/post-processing. A chaotic jerk oscillator is a deterministic source of randomness that potentially offers robust and highly random chaotic signals and exhibits a distinctive property of smoothly balanced-to-unbalanced alternation of double-scroll attractors. The continuous-time 2nd-order ΔΣ modulator is introduced as a mixed-signal interface in order to increase a resolution of random bit sequences while no extra clock is required...
June 2018: Chaos
Khaled M Saad, Abdon Atangana, Dumitru Baleanu
In this paper, we extend the model of the Burgers (B) to the new model of time fractional Burgers (TFB) based on Liouville-Caputo (LC), Caputo-Fabrizio (CF), and Mittag-Leffler (ML) fractional time derivatives, respectively. We utilize the Homotopy Analysis Transform Method (HATM) to compute the approximate solutions of TFB using LC, CF, and ML in the Liouville-Caputo sense. We study the convergence analysis of HATM by computing the interval of the convergence, the residual error function (REF), and the average residual error (ARE), respectively...
June 2018: Chaos
Piyush Grover, Kaivalya Bakshi, Evangelos A Theodorou
Empirically derived continuum models of collective behavior among large populations of dynamic agents are a subject of intense study in several fields, including biology, engineering, and finance. We formulate and study a mean-field game model whose behavior mimics an empirically derived nonlocal homogeneous flocking model for agents with gradient self-propulsion dynamics. The mean-field game framework provides a non-cooperative optimal control description of the behavior of a population of agents in a distributed setting...
June 2018: Chaos
I A Shepelev, G I Strelkova, V S Anishchenko
We study the spatiotemporal dynamics of coupled Lorenz systems with nonlocal interaction and for small values of the coupling strength. It is shown that due to the interaction the effective values of the control parameters can shift and the classical quasi-hyperbolic Lorenz attractor in an isolated element is transformed to a nonhyperbolic one. In this case, the network becomes multistable that is a typical property of nonhyperbolic chaotic systems. This fact gives rise to the appearance of chimera-like states, which have not been found in the studied network before...
June 2018: Chaos
A Perinelli, D E Chiari, L Ricci
Assessing brain connectivity makes up a major issue in the field of network dynamics and neuroscience. Conventional experimental techniques are based on functional imaging and magnetoencephalography, allowing to reconstruct the activity of relatively small brain volume elements. A common approach to identify networks consists in singling out sets of elements that maintain a correlated activity over time. Despite the general consensus that these networks are detectable on a time window of 10 s, no study is presently available on the distribution and thus the reliability of this time scale...
June 2018: Chaos
Christoph Bandt, Dmitry Mekhontsev
By slight modification of the data of the Sierpiński gasket, keeping the open set condition fulfilled, we obtain self-similar sets with very dense parts, similar to fractals in nature and in random models. This is caused by a complicated structure of the open set and is revealed only under magnification. Thus, the family of self-similar sets with separation condition is much richer and has higher modelling potential than usually expected. An interactive computer search for such examples and new properties for their classification are discussed...
June 2018: Chaos
Vishnu R Unni, Abin Krishnan, R Manikandan, Nitin B George, R I Sujith, Norbert Marwan, Jürgen Kurths
We use complex network theory to investigate the dynamical transition from stable operation to thermoacoustic instability via intermittency in a turbulent combustor with a bluff body stabilized flame. A spatial network is constructed, representing each of these three dynamical regimes of combustor operation, based on the correlation between time series of local velocity obtained from particle image velocimetry. Network centrality measures enable us to identify critical regions of the flow field during combustion noise, intermittency, and thermoacoustic instability...
June 2018: Chaos
Liyuan Zhang, Denggui Fan, Qingyun Wang
Studies on the structural-functional connectomes of the human brain have demonstrated the existence of synchronous firings in a specific brain network motif. In particular, synchronization of high-frequency oscillations (HFOs) has been observed in the experimental data sets of temporal lobe epilepsy (TLE). In addition, both clinical and experimental evidences have accumulated to demonstrate the effect of electrical stimulation on TLE, which, however, remains largely unexplored. In this work, we first employ our previously proposed dentate gyrus (DG)-CA3 network model to investigate the influence of an external electrical stimulus on the HFO transitions...
June 2018: Chaos
Justine Wolter, Benedict Lünsmann, Xiaozhu Zhang, Malte Schröder, Marc Timme
Spreading phenomena on networks are essential for the collective dynamics of various natural and technological systems, from information spreading in gene regulatory networks to neural circuits and from epidemics to supply networks experiencing perturbations. Still, how local disturbances spread across networks is not yet quantitatively understood. Here, we analyze generic spreading dynamics in deterministic network dynamical systems close to a given operating point. Standard dynamical systems' theory does not explicitly provide measures for arrival times and amplitudes of a transient spreading signal because it focuses on invariant sets, invariant measures, and other quantities less relevant for transient behavior...
June 2018: Chaos
Çağrı Haksöz, Konstantinos Katsikopoulos, Gerd Gigerenzer
We review empirical evidence from practice and general theoretical conditions, under which simple rules of thumb can help to make operations flexible and robust. An operation is flexible when it responds adaptively to adverse events such as natural disasters; an operation is robust when it is less affected by adverse events in the first place. We illustrate the relationship between flexibility and robustness in the context of supply chain risk. In addition to increasing flexibility and robustness, simple rules simultaneously reduce the need for resources such as time, money, information, and computation...
June 2018: Chaos
Wei Bao, George Michailidis
Modeling information diffusion on networks is a timely topic due to its significance in massive online social media platforms. Models motivated by disease epidemics, such as the Susceptible-Infected-Removed and Susceptible-Infected-Susceptible (SIS), ones have been used for this task, together with threshold models. A key limitation of these models is that the intrinsic time value of information is not accounted for, an important feature for social media applications, since "old" piece of news does not attract adequate attention...
June 2018: Chaos
Markus Quade, Markus Abel, J Nathan Kutz, Steven L Brunton
Big data have become a critically enabling component of emerging mathematical methods aimed at the automated discovery of dynamical systems, where first principles modeling may be intractable. However, in many engineering systems, abrupt changes must be rapidly characterized based on limited, incomplete, and noisy data. Many leading automated learning techniques rely on unrealistically large data sets, and it is unclear how to leverage prior knowledge effectively to re-identify a model after an abrupt change...
June 2018: Chaos
Fang Wang, Lin Wang, Yuming Chen
In order to analyze lagged correlations hidden in complex systems, we propose a new method by incorporating a time-lagged operator into the multi-affine height correlation analysis (MA-HCA). Application of this lagged MA-HCA to an artificially simulated example indicates that the method is feasible to successfully detect the existence of lagged correlations. We then apply this method to explore lagged correlations in series arising from three real-world complex systems.
June 2018: Chaos
Y N Kyrychko, I B Schwartz
The paper addresses the problem of calculating the noise-induced switching rates in systems with delay-distributed kernels and Gaussian noise. A general variational formulation for the switching rate is derived for any distribution kernel, and the obtained equations of motion and boundary conditions represent the most probable, or optimal, path, which maximizes the probability of escape. Explicit analytical results for the switching rates for small mean time delays are obtained for the uniform and bi-modal (or two-peak) distributions...
June 2018: Chaos
A D Fragkou, T E Karakasidis, E Nathanail
In this study, we present results of the application of nonlinear time series analysis on traffic data for incident detection. More specifically, we analyze daily volume records of Attica Tollway (Greece) collected from sensors located at various locations. The analysis was performed using the Recurrence Plot (RP) and Recurrence Quantification Analysis (RQA) method of the volume data of the lane closest to the median. The results show that it is possible to identify, through the abrupt change of the dynamics of the system revealed by RPs and RQA, the occurrence of incidents on the freeway and differentiate from recurrent traffic congestion...
June 2018: Chaos
Alessandro Loppini, Morten Gram Pedersen
Pancreatic β-cells show multiple intrinsic modes of oscillation with bursting electrical activity playing a crucial role. Bursting is seen both in experimentally isolated β-cells as well as in electrically coupled cells in the pancreatic islets, but the burst period is typically an order of magnitude greater in coupled cells. This difference has previously been attributed to noisier dynamics, or perturbed electrophysiological properties, in isolated β-cells. Here, we show that diffusive coupling alone can extend the period more than ten-fold in bursting oscillators modeled with a so-called phantom burster model and analyze this result with slow-fast bifurcation analysis of an electrically coupled pair of cells...
June 2018: Chaos
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