Synchronization Phenomena Research Articles

ЛИВЕНЦОВСКАЯ И КАРАТАЕВСКАЯ КРЕПОСТИ: ЛИНИИ СИНХРОНИЗАЦИИ С ПАМЯТНИКАМИ СЕВЕРНОГО КАВКАЗА И СЕВЕРНОГО ПРИЧЕРНОМОРЬЯ

The article presents the result of a comparative analysis of the materials of the kamensko-liventsovskaya group of monuments the final of Middle Bronze Age. The discovery of Liven-tsovskaya and Karataevskaya fortresses in the lower reaches of the Don in the 1960s by S.N. Bratchenko allowed a new look at the antiquities of the final of Middle Bronze Age. The two forti-fications, situated on the right bank of the Mertvyi Donets river, are a single defensive complex. When comparing the Lower Don fortress materials with finds from the Kamenka settlement in the Eastern Crimea, S.N. Bratchenko came to the conclusion that they differ from other synchronous phenomena. As a result, the scientist distinguishes these monuments into a separate culture – the kamensko-liventsovskaya group. Similar materials were also found in the settlement and burial complexes of the North Caucasus. The discovery of new monuments of the final of Middle Bronze Age in the Northern Black Sea area and the North Caucasus made it possible to consider the ka-mensko-liventsovskaya monuments differently in the general interconnection of the post-Cathacombian cultures. On the basis of comparative and comparative method similar to the ka-mensko-liventsovskaya materials are given and as a consequence the reconstruction of possible contacts between the territories of the Lower Don – Northern Black Sea Region – Northern Cauca-sus.

Nonlinear resonant responses of hyperelastic cylindrical shells with initial geometric imperfections

The resonant responses of the hyperelastic cylindrical shell with the initial geometric imperfections are investigated by considering both geometric and material nonlinearities. The hyperelastic cylindrical shell is subjected a radial harmonic excitation. Based on Donnell's theory, hyperelastic constitutive relations and Lagrange equation, the differential governing equations of motion are derived for the hyperelastic cylindrical shell with the initial geometric imperfections. Using the multiple scale method, the perturbation analysis for the governing equations of motion is conducted under the 2:1 internal resonance condition. The amplitude-frequency and force-amplitude response curves are obtained for the hyperelastic cylindrical shell. The effect of different parameters on the linear frequencies, amplitude-frequency response curves, force-amplitude response curves and chaotic responses of the hyperelastic cylindrical shell are discussed. The numerical results indicate that the existence of the geometric imperfections leads to the increase of the linear frequencies of the hyperelastic cylindrical shell. The amplitude-frequency response curves have the typical double-jumping phenomena and the response amplitudes increase with the increase of the external excitation amplitudes. The imperfection amplitudes, imperfection forms and structure parameters have the obvious influences on the resonant peaks evolutions. The vibrations of the first-order and second-order modes have the synchronization phenomena. With the changes of the parameters, the dynamic responses of the hyperelastic cylindrical shell with the imperfections change the period to chaotic vibrations alternately.

Synchronization and multistability in a network of diffusively coupled laser models

Synchronization phenomena refer to the emergence of common temporal patterns among clusters of interacting units in a complex network. In information transmission, lasers’ synchronization plays a key role in facilitating information communication. This paper is devoted to studying the synchronization of globally coupled identical laser models via the linear and nonlinear forms of diffusive couplings. In this regard, the master stability function and time-averaged synchronization error are employed as the analytical and numerical approaches to examine complete synchronization. Apart from the complete synchrony, the constructed networks are explored to find other synchronization patterns and multistability. The results obtained from the master stability function analysis, which are further approved by the numerical outcomes, show that when coupled through the linear diffusive function, the interacting laser models achieve complete synchrony in a small value of the coupling parameter. However, in the nonlinear case, complete synchronization cannot be attained. Moreover, multistability can be observed in different network states, including cluster synchronization, chimera, and solitary states.

A modification to the Kuramoto model to simulate epileptic seizures as synchronization

The Kuramoto model was developed to describe the coupling of oscillators, motivated by the natural synchronization phenomena. We are interested in modeling an epileptic seizure considering it as the synchronization of action potentials using and modifying this model. In this article, we propose to modify this model, changing the constant coupling force for a function with logistic growth to simulate the onset and epileptic seizure level in an adult male rat caused by the administration of lithium–pilocarpine. Later, we select some frequencies and their respective amplitude values using an algorithm based on the fast Fourier transform (FFT) from an electroencephalography signal when the rat is in basal conditions. Then, we take these values as the natural frequencies of the oscillators in the modified Kuramoto model, considering every oscillator as a single neuron to simulate the emergence of an epileptic seizure numerically by increasing the synchronization value in the coupling function. Finally, using Dynamic Time Warping algorithm, we compare the simulated signal by the Kuramoto model with an FFT approximation of the epileptic seizure.

Desynchronization and Oscillatority in Excitable FitzHugh-Nagumo Networks

Study of dynamics of complex networked systems is one of the relevant problems. Networked systems can be in various states, ranging from complete synchronization, when all systems in the network are coherent, to complete desynchronization, i.e. complete incoherence in the functioning of systems. Synchronization phenomenon has already been well studied, namely, the mathematical definitions of synchronization are introduced, algorithms of studying synchronization are proposed, and synchronization conditions of various types of networked systems are established. Whereas a few works are devoted to the study of desynchronization nowadays. This paper introduces output desynchronization notion for networks of nonlinear systems. The definitions about Yakubovich oscillatority are considered and the link between oscillatority and desynchronization in networks of excitable nonlinear systems is established. Excitable systems are stable; therefore, they do not generate oscillations. Adding couplings between such systems can lead to occurrence of oscillations. The conditions about oscillatority in diffusively coupled networks of FitzHugh-Nagumo systems, which are the simplest neuron models, are derived. Firstly, the case of the simplest network of two coupled systems is considered, and afterwards, obtained result is generalized for the case of several systems. Laplace matrix spectrum plays crucial role in dynamics of such networks. The condition that connects the parameters of the uncoupled system in the network and the eigenvalues of the Laplace matrix, is obtained which determines whether the network is oscillatory or not. The number of systems that generate oscillations in such a network depends on the number of eigenvalues of the Laplace matrix that satisfy the obtained conditions. Obtained analytical results are confirmed by simulation. The results of simulation of complete desynchronization in the network, when all systems begin to oscillate, as well as a chimera-like state, in which only a part of the systems oscillates, while the other part are rest, are presented.

Synchronization of Frequency-Modulated Multiagent Systems

Oscillation synchronization phenomenon is widely observed in natural systems through frequency modulated signals, especially in biological neural networks. Frequency modulation is also one of most widely used technologies in engineering. However, due to the technical difficulty, oscillations are always simplified as unmodulated sinusoidal-like waves in studying the synchronization mechanism in the bulky literature over the decades. It lacks mathematical principles, especially systems and control theories, for frequency modulated multi-agent systems. This paper aims to bring a new formulation of synchronization of frequency modulated multi-agent systems. It develops new tools to solve the synchronization problem by addressing three issues including frequency observation in nonlinear frequency modulated oscillators subject to network influence, frequency consensus via network interaction subject to observation error, and a well placed small gain condition among them. The architecture of the paper consists of a novel problem formulation, rigorous theoretical development, and numerical verification.

Experimental observation of chimera states in spiking neural networks based on degenerate optical parametric oscillators

The phenomenon of partial synchronization has attracted significant interest in the field of nonlinear dynamics, largely due to observations of related phenomena in real-world situations. In particular, the coexistence of synchronized and desynchronized phases, known as a chimera state, has been the subject of intense study. In this work, we experimentally demonstrate that networks of identical photonic spiking neurons based on coupled degenerate optical parametric oscillators can exhibit various chimera states in which, depending on their local synchronization and desynchronization, different kinds of spiking dynamics can develop in a self-organized manner. Even when only a static interaction is implemented, the spiking mode of photonic neurons can be spontaneously and adaptively changed between the Class-I and Class-II modes classified by A. L. Hodgkin. This spontaneous spiking-mode shift induces a significant change in the spiking frequency despite all neurons having the same natural spiking frequency, which encourages the generation of chimera states.

Synchronization of the Circadian Rhythms with Memory: A Simple Fractional-Order Dynamical Model Based on Tow Coupled Oscillators

Disruptions of the circadian rhythm are associated with internal desynchronization. It affects some internal functions of our body and behavior that are important to our health. Our modern lifestyle has contributed to millions of people developing some circadian rhythm disruptions, making the subject very important clinically as well as economically. Motivated by studying a simple mathematical model that can reveal some features of internal synchronization desynchronization, in this contribution, we extend the coupling oscillator phase model proposed by Strogatz [14] in the sense that memory is considered in the modeling. Such memory is a result of the introduction of Caputo-type fractional derivatives in the coupling oscillators’ phase model dynamics, resulting in a fractional phase model. We show that the proposed fractional coupling oscillator phase model is well-posed. Furthermore, we analyzethe synchronization phenomena. We obtain the synchronized solutions explicitly when the memory is equally distributed between the oscillators. In contrast, when distinct levels of memory are imposed in the modeling, we obtain lower and upper bounds because any existing synchronized solution must be confined in between. We present numerical realizations that support the theoretical findings in great detail.

Synchronous impact phenomenon of a high-dimension complex nonlinear dual-rotor system subjected to multi-frequency excitations

Synchronous impact phenomenon of a high-dimension complex nonlinear dual-rotor system subjected to multi-frequency excitations

Characterization of Leaf Transcriptome in a Tropical Tree Species, <i>Shorea curtisii</i>, over a Flowering Season

General flowering (GF) is a synchronous flowering phenomenon in the Southeast Asian tropical rainforests that occurs at irregular intervals of multiple years. While in this study, the leaf transcriptome of a GF species, Shorea curtisii obtained from three-time points – before and after floral initiation, and post-flowering stage – was sequenced, the unpredictable intervals of GF raise conservation concerns for these under-researched forests with rich economically and ecologically important species. We assembled 243,759,478 sequencing reads into 39,943 non-redundant unigenes including 677 putative homologs of Arabidopsis thaliana flowering-related genes. Differential expression analysis conducted on pairwise comparisons of the time points identified 930 differentially expressed unigenes, which includes 17 flowering-related homologs. The differential expression of unigenes with significant enrichments of functions related to drought corroborated the involvement of drought as an environmental cue for GF, with the outcomes of this study offering an insight into the conservation of floral regulatory genes and pathways in Shorea and possibly being used as a model to better understand the floral initiation cues and regulation of GF trees.

Synchronization of persistent oscillations in spin systems with nonlocal dissipation

We explore the synchronization phenomenon in the quantum few-body system of spins with the nonlocal dissipation. Without the external driving, we find that the system can exhibit stable oscillatory behaviors in the long-time dynamics accompanied by the appearance of the purely imaginary eigenvalues of the Liouvillian. Moreover, the oscillations of the next-nearest-neighboring spins are completely synchronized, which is revealed by the quantum trajectory analysis within the stochastic Schr\"odinger equation. The possibility of the appearance of the long-time oscillations in an infinite-size lattice by means of cluster mean-field approximation is also discussed.

Global attractors and synchronization of coupled critical Lamé systems with nonlinear damping

We investigate the global attractors and synchronization phenomenon of a coupled critical Lamé system defined on a smooth bounded domain Ω⊂R3 with nonlinear damping and nonlinear forces of critical growth. The existence of a unique and finitely dimensional global attractor Aϰ is proved in the natural energy space H=[D((−Δe)12)]2×[(L2(Ω))3]2, where ϰ is the coupling parameter and Δe is the Lamé operator. This attractor is further proved to be smooth in the regular space [(H2(Ω))3∩(H01(Ω))3]2×[(H01(Ω))3]2. We also show that the coupled Lamé system can be reduced to a single one when ϰ tends to infinity. Then we can compare dynamics of the coupled and single systems by proving the upper-semicontinuity of their attractors in Hδ=[(H2−δ(Ω))3∩(H01−δ(Ω))3]2×[(H01−δ(Ω))3]2 for any δ∈(0,1) as ϰ→∞. These results are finally used to study the asymptotic and exponential synchronization phenomena for the coupled Lamé system.

Monitoring Molecular Structure Changes of Cow and Camel Milk Mixtures during Coagulation: A Study Based on TPA and 2DCOS-MIR Spectroscopy

The aim of the present study is to evaluate the potential of mid-infrared spectroscopy in combination with two-dimensional correlation spectroscopy (2DCOS) and partial least squares discriminant analysis (PLS-DA) to monitor molecular structure evolution of milk mixtures of two species (cow and camel) during enzymatic coagulation. Molecular structure changes and texture characteristics were investigated on five different milk formulations by mixing camel milk (CaM) and cow milk (CM) (i.e., CaM, CaM3:CM1, CaM1:CM1, CaM1:CM3, and CM, (v/v)). Regarding MIR spectroscopy, two spectral regions were considered to monitor milk coagulation, the fatty acid acyl-chain region (3000–2800 cm−1) and the protein region (1700–1500 cm−1). Different formulation dissimilarities were revealed through the synchronous 2DCOS spectra and their respective auto-peaks. Moreover, using the cross-peak symbols of the synchronous and asynchronous spectra helps to establish the sequence of molecular structure modifications during coagulation. Finally, the analysis of the 2DCOS-MIR synchronous and asynchronous maps by PLS-DA gave good discriminant accuracy (88 to 100%) between each formulation. Those results highlighted that different synchronous and asynchronous chemical phenomena occurred during milk coagulation depending on the milk formulation. Texture attributes were influenced by camel milk ratio in mixtures based on the initial composition of milks. Samples containing more than 50% of CM showed significantly higher hardness compared to pure CaM and CaM3:CM; however, CM gel displayed lower springiness contrary to CaM. Textural characteristics of the resulted gels also confirmed that 2DCOS MIR observations are consistent with textural observations of the gels obtained after milk mixtures coagulation.

An extended Hilbert transform method for reconstructing the phase from an oscillatory signal

Rhythmic activity is ubiquitous in biological systems from the cellular to organism level. Reconstructing the instantaneous phase is the first step in analyzing the essential mechanism leading to a synchronization state from the observed signals. A popular method of phase reconstruction is based on the Hilbert transform, which can only reconstruct the interpretable phase from a limited class of signals, e.g., narrow band signals. To address this issue, we propose an extended Hilbert transform method that accurately reconstructs the phase from various oscillatory signals. The proposed method is developed by analyzing the reconstruction error of the Hilbert transform method with the aid of Bedrosian’s theorem. We validate the proposed method using synthetic data and show its systematically improved performance compared with the conventional Hilbert transform method with respect to accurately reconstructing the phase. Finally, we demonstrate that the proposed method is potentially useful for detecting the phase shift in an observed signal. The proposed method is expected to facilitate the study of synchronization phenomena from experimental data.

Step-adaptive sound guidance enhances locomotor-respiratory coupling in novice female runners: A proof-of-concept study.

Many runners struggle to find a rhythm during running. This may be because 20-40% of runners experience unexplained, unpleasant breathlessness at exercise onset. Locomotor-respiratory coupling (LRC), a synchronization phenomenon in which the breath is precisely timed with the steps, may provide metabolic or perceptual benefits to address these limitations. It can also be consciously performed. Hence, we developed a custom smartphone application to provide real-time LRC guidance based on individual step rate. Sixteen novice-intermediate female runners completed two control runs outdoors and indoors at a self-selected speed with auditory step rate feedback. Then, the runs were replicated with individualized breath guidance at specific LRC ratios. Hexoskin smart shirts were worn and analyzed with custom algorithms to estimate continuous LRC frequency and phase coupling. LRC guidance led to a large significant increase in frequency coupling outdoor from 26.3 ± 10.7 (control) to 69.9 ± 20.0 % (LRC) "attached". There were similarly large differences in phase coupling between paired trials, and LRC adherence was stronger for the indoor treadmill runs versus outdoors. There was large inter-individual variability in running pace, preferred LRC ratio, and instruction adherence metrics. Our approach demonstrates how personalized, step-adaptive sound guidance can be used to support this breathing strategy in novice runners. Subsequent investigations should evaluate the skill learning of LRC on a longer time basis to effectively clarify its risks and advantages.

Synchronization of machine learning oscillators in complex networks

We study synchronization phenomena in complex networks in terms of machine learning oscillators without conventional dynamical equations. Specifically, we adopt an effective machine learning technique known as reservoir computing for modeling dynamical systems of interest. By constructing a coupled configuration, we show that a collection of coupled reservoir oscillators are in identical synchrony over a wider window of coupling strengths. We find that the geometrical and dynamical properties of synchronous orbits are in excellent agreement with that of the learned dynamical system. Remarkably, through this synchronization scheme, we successfully recover an almost identical bifurcation behavior of an observed system via merely its chaotic dynamics. Our work provides an alternative framework for studying synchronization phenomena in nature when only observed data are available.

Synchronization in Pairs of Opto-Thermally Driven Mechanically Coupled Micro-Oscillators

We study the phenomenon of synchronization in pairs of doubly clamped, mechanically coupled silicon micro-oscillators. A continuous-wave laser beam is used to drive the micro-beams into limit cycle oscillations and to detect the oscillations using interferometry. Devices of different dimensions are used to introduce frequency detuning, and short silicon bridges connecting the micro-beams are used as mechanical coupling between the oscillators. The region of synchronization is plotted for the MEMS system in the detuning vs. coupling parameter space and compared with the numerical analysis of a corresponding, lumped-parameter model. Three states of oscillations are observed i.e. the drift state, quasi-periodic state, and the synchronized state. The numerical model also distinguishes between in-phase and out-of-phase synchronization where out-of-phase synchronization is observed at low coupling strengths and low frequency detuning. [2022-0140]

Asymmetric adaptivity induces recurrent synchronization in complex networks.

Rhythmic activities that alternate between coherent and incoherent phases are ubiquitous in chemical, ecological, climate, or neural systems. Despite their importance, general mechanisms for their emergence are little understood. In order to fill this gap, we present a framework for describing the emergence of recurrent synchronization in complex networks with adaptive interactions. This phenomenon is manifested at the macroscopic level by temporal episodes of coherent and incoherent dynamics that alternate recurrently. At the same time, the dynamics of the individual nodes do not change qualitatively. We identify asymmetric adaptation rules and temporal separation between the adaptation and the dynamics of individual nodes as key features for the emergence of recurrent synchronization. Our results suggest that asymmetric adaptation might be a fundamental ingredient for recurrent synchronization phenomena as seen in pattern generators, e.g., in neuronal systems.

The Role of Damping Rate Amplitude in the Synchronization of Two Coupled Oscillators

In this paper, we investigate the synchronization phenomenon between two Spin-transfer Torque Nanooscillators (STNOs) of different frequencies in two pillar systems under vortex configuration detunings or driving frequencies. The oscillators’ mutual synchronization occurs through magnetic dipolar interaction. Our micromagnetic simulations show that an amplitude fluctuation referred to as [Formula: see text] has a significant impact on determining the synchronization frequency. The evolution of frequency and amplitude fluctuation rate in two different oscillator sizes versus external perpendicular field will be compared and discussed. Our results reveal that the oscillator with lower [Formula: see text], referred to as the “Leader” oscillator, leads the synchronization process. As such, the “follower” oscillator adjusts its frequency as to that of the “Leader”, thus achieving synchronization. We believe that taking [Formula: see text] into consideration can help in controlling synchronization frequencies in future building blocks of any network multi-array spintronics’ devices.

Combination resonance and primary resonance characteristics of a dual-rotor system under the condition of the synchronous impact of the inter-shaft bearing

The internal structure of many aero-engines is designed with a dual-rotor system. Up to now, there have been few studies on the influence of aerodynamic excitation on the dual-rotor system. The phenomenon of synchronous impact may occur when the frequency of the aerodynamic excitation force of the fan blade is close to the characteristic frequency of the inter-shaft bearing. This paper investigates the dynamic characteristics of a dual-rotor system under the condition of synchronous impact. The system's motion equations are formulated considering the complex nonlinearities of the inter-shaft bearing, such as Hertz contact force of 10/9 exponential function, clearance, and periodic varying compliance. In addition, the inter-shaft bearing with a local defect is considered. The fan blade’s aerodynamic excitation force is modeled by synthesizing multiple harmonic excitation forces, the amplitudes of which are obtained by the Fourier series expansion. Numerical simulations are employed to get the dynamic responses of the system. The results show that the dynamic characteristic of the dual-rotor system at the primary resonance caused by the high-pressure (H.P.) rotor is not changed by the aerodynamic excitation force, while the primary resonance caused by the low-pressure (L.P.) rotor increases significantly. However, three aerodynamic resonances of the amplitude-frequency response of the dual-rotor system are emerging in the low-frequency region (124, 146 and 186 rad/s). When the synchronous impact phenomenon occurs, the amplitude of the three resonance peaks will increase twice compared to the original status, leading to a doubled increase in the dynamic load of the inter-shaft bearing. The characteristics of the dual-rotor system affected by the parameters such as initial phase difference of local defect, rotor eccentricity of system, clearance of inter-shaft bearing, and the stiffness and damping of supports are discussed in detail. The results obtained provide a deep insight into the mechanism of synchronous impact.