Synchronization Region Research Articles

Impact of multiplexing noise on multilayer networks of bistable maps

We explore numerically the complex dynamics of multilayer networks (consisting of three and one hundred layers) of cubic maps in the presence of noise-modulated interlayer coupling (multiplexing noise). The coupling strength is defined by independent discrete-time sources of color Gaussian noise. Uncoupled layers can demonstrate different complex structures, such as double-well chimeras, coherent and spatially incoherent regimes. Regions of partial synchronization of these structures are identified in the presence of multiplexing noise. We elucidate how synchronization of a three-layer network depends on the initially observed structures in the layers and construct synchronization regions in the plane of multiplexing noise parameters “noise spectrum width – noise intensity”. It is shown that in a hundred-layer network, clusters of synchronized layers can be formed at certain optimal values of multiplexing noise parameters. The performed numerical studies confidently indicate that the spatial dynamics of multilayer networks can be controlled by varying multiplexing noise parameters.

Synchronization and limit cycles in a simple contagion model with time delays

We examine a system of N=2 coupled non-linear delay-differential equations representing financial market dynamics. In such time delay systems, coupled oscillations have been derived. We linearize the system for small time delays and study its collective dynamics. Using analytical and numerical solutions, we obtain the bifurcation diagrams and analyze the corresponding regions of amplitude death, phase locking, limit cycles and market synchronization in terms of the system frequency-like parameters and time delays. We further numerically explore higher order systems with N>2, and demonstrate that limit cycles can be maintained for coupled N−asset models with appropriate parameterization.

Structural multistability for multi-speed wind energy harvesting from vortex-induced vibrations

Abstract Piezoelectric energy harvesters utilizing vortex-induced vibrations (VIV) have been extensively studied for converting wind energy into usable power for microelectronics. In this work, we explore the use of structural bistability to increase the range of flow speeds over which energy can be harvested without the need for complicated assemblies. We propose a harvester system featuring a piezoelectric transducer bonded to a cantilevered bistable composite laminate, which has two distinct equilibrium shapes at room temperature. To enhance the VIV, we attach a cylindrical bluff body to the free edge of the harvester. The structure’s inherent bistability allows for high power generation at two different flow speeds, contrasting with the single synchronization region typical of linear piezoelectric harvesters. We develop a reduced-order model to predict power output across varying flow speeds and validate these predictions through wind tunnel experiments, showing good agreement. Furthermore, we conduct a parametric study to optimize the model parameters for maximum power output. Our results demonstrate that the bistable harvester can generate up to 4.5 mW of power over a wind speed range of 9.3 m s−1–11.7 m s−1, outperforming the limited speed range of traditional linear VIV-based harvesters. This work underscores the potential to design VIV-based energy harvesters capable of operating efficiently across multiple flow speed ranges using a single structure with its dual stable configurations.

Secure impulsive cluster synchronization control of complex dynamical networks with parameter mismatches under deception attacks

The issue of secure cluster synchronization (SCS) of complex dynamical networks (CDNs) with parameter mismatches under deception attacks is investigated in this article. Firstly, the deception attacks are supposed to inject false information into controller-to-actuator channels, while the occurrences of deception attack are always subject to Bernoulli distribution. Secondly, an improved pinning impulsive control strategy is designed. The impulsive gain in the control strategy is take from a new range. Moreover, we obtain the estimation of synchronization error upper bound and boundaries of secure synchronization region. The synchronization error will converge to a bounded ball that depends on attack energy at a exponential rate. The CDNs without deception attacks under pinning impulsive control can achieve complete cluster synchronization. Finally, two numerical examples with 20 nodes based on MATLAB software are presented to demonstrate the effectiveness of the theoretical results.

Synchronization patterns in a network of diffusively delay-coupled memristive Chialvo neuron map

The inescapable presence of time delay in numerous real-world systems, particularly in neuronal networks, prompts an exploration of its impact on synchronization dynamics. This study employs memristive Chialvo maps to capture the local dynamics of network nodes, while connections are homogeneously described by a linear diffusive function—referred to as electrical couplings in mathematical neuroscience—incorporating a specific time delay. Using Master stability functions (MSFs), analytical assessments are conducted to examine the stability of synchronous solutions, a validation supported by time-averaged synchronization error calculations. This research reveals the time delay's influence on the synchrony, making the synchronous state dependent on the coupling parameter's strength. The behavior of the synchronization manifold is systematically probed across synchronous and asynchronous regions analyzed by the MSF analysis. Lastly, an investigation involving a neuronal network with a global coupling configuration reveals that neurons have a tendency to organize into clusters with distinct time lags.

Optical chaos synchronization in a cascaded injection experiment.

We experimentally study the synchronization of chaos generated by semiconductor lasers in a cascade injection configuration, i.e., a tunable master laser is used to generate chaos by optical injection in a transmitter laser that injects light into a receiver laser. Chaos synchronization between the transmitter and the receiver lasers is achieved with a correlation coefficient of 90% for a measurement bandwidth up to 35 GHz. Two parameter regions of good synchronization are found, corresponding to the alignment of the oscillation frequencies of the receiver laser with either the transmitter laser or the master laser.

Synchronization in a higher-order neuronal network with blinking interactions

The synchronization of higher-order networks presents a fascinating area of exploration within nonlinear dynamics and complex networks. Simultaneously, growing research interest focuses on uncovering synchronization dynamics in time-varying networks with time-dependent coupling structures, reflecting their prevalence in real-world systems like neuronal networks. Motivated by this, the present study delves into the synchronization phenomenon within a higher-order network incorporating a blinking coupling scheme. Blinking coupling is an on–off switching coupling that has been demonstrated to enhance synchronization effectively. Its efficacy stems from ensuring synchronization, as the master stability function (MSF) follows a linear pattern. In this study, our objective is to investigate such a time-varying coupling scheme in a higher-order network configuration. We investigate the influence of coupling parameters and blinking frequency on synchronization behavior. Notably, our findings demonstrate that as the blinking frequency increases, the network exhibits a gradual convergence toward the behavior of the average network. Furthermore, leveraging the analytical framework of MSF and the average synchronization error, we provide analytical and numerical evidence confirming that the MSF pattern within the average network transforms into a linear function. The synchronous and asynchronous regions also exhibit a clear separation demarcated by a linear curve across the coupling parameter space. Moreover, our results suggest that incorporating higher-order interactions fosters enhanced synchrony by effectively scaling the synchronization patterns to lower coupling parameter values.

The effect of nonlinear diffusive coupling on the synchronization of coupled oscillators

This paper examines the impact of nonlinear coupling on the synchronization of interconnected oscillators. Various powers of diffusive coupling are explored to introduce nonlinear effects, and the results are contrasted with those of linear diffusive coupling. The study employs three representative chaotic systems, namely, the Lorenz, Rössler, and Hindmarsh-Rose systems. Findings indicate that nonlinear couplings with power below one result in synchronization at lower coupling strengths. Additionally, the critical coupling strength reduces as the coupling power decreases. However, the synchronization region undergoes changes and becomes bounded. Conversely, for powers exceeding one, networks are either unable to synchronize or require higher coupling strengths compared to linear coupling.

Exploring synchronizability of complex dynamical networks from edges perspective

With the rapid development of network information technology, synchronization problem of complex dynamical networks has garnered extensive attention. Current research predominantly concentrates on analyzing synchronizability and synchronization control in the complex dynamical networks with static edge weights or single weight attribute connections. However, there is limited research on networks characterized by variable weights and multiple weighted connections. This study addresses this gap by analyzing the synchronizability of such complex networks. In this paper, we investigate the synchronizability of two types of networks: weight-variable complex dynamical networks and multi-weighted complex dynamical networks. Considering the evolution of network weights, the synchronizability of complex dynamical network with weight-variable is investigated, the master stability equation, synchronizability criteria of the network are derived, and experiments are used to substantiate the validity of our findings. Our study then shifts to multi-weighted complex networks. Take the Rössler oscillators as node dynamics, we explore the impact of different inner coupling matrices on synchronization types under both unknown and known topologies. Moreover, we extend our study to scenarios with different coupling strengths. The analysis reveals that the inner coupling matrix influences the network’s synchronization region type. Interestingly, the clarity or ambiguity of network topologies does not markedly affect the synchronization region type. Furthermore, our analysis indicates a correlation between the synchronization region boundaries of multi-weighted complex networks and those of their single-weighted counterparts capable of synchronization.

Stability analysis of synchronization in long-range temporal networks using theory of dichotomy.

Most of the previous studies on the stability analysis of synchronization in static or time-varying networks are based on the master stability function approach, which is a semi-analytical concept. The necessary and sufficient conditions for synchronization in time-varying networks are challenging problems since the last few years. We focus on the stability analysis of synchronization in time-varying networks, particularly long-range networks. The use of dichotomy theory to derive sufficient conditions for synchronization in this context is an interesting approach. The incorporation of long-range interactions adds complexity and might lead to larger regions of synchronization, providing valuable insights into the dynamics of such networks. Analyzing the co-action of the time-varying nature in the network topology and long-range interactions is a relevant and challenging task, especially when the network is not synchronized. This work appears to explore the interplay between these factors and their impact on synchronization. Additionally, the numerical study considering long-range connections governed by a power-law within the framework of an Erdös-Rényi random network is a practical way to validate and test the analytical results. It is good to see that we are exploring the effects of varying parameters such as rewiring probability, coupling strength, and power-law exponent on the synchronization state.

Nonlinearity-Induced Asymmetric Synchronization Region in Micromechanical Oscillators.

Synchronization in microstructures is a widely explored domain due to its diverse dynamic traits and promising practical applications. Within synchronization analysis, the synchronization bandwidth serves as a pivotal metric. While current research predominantly focuses on symmetric evaluations of synchronization bandwidth, the investigation into potential asymmetries within nonlinear oscillators remains unexplored, carrying implications for sensor application performance. This paper conducts a comprehensive exploration employing straight and arch beams capable of demonstrating linear, hardening, and softening characteristics to thoroughly scrutinize potential asymmetry within the synchronization region. Through the introduction of weak harmonic forces to induce synchronization within the oscillator, we observe distinct asymmetry within its synchronization range. Additionally, we present a robust theoretical model capable of fully capturing the linear, hardening, and softening traits of resonators synchronized to external perturbation. Further investigation into the effects of feedback strength and phase delay on synchronization region asymmetry, conducted through analytical and experimental approaches, reveals a consistent alignment between theoretical predictions and experimental outcomes. These findings hold promise in providing crucial technical insights to enhance resonator performance and broaden the application landscape of MEMS (Micro-Electro-Mechanical Systems) technology.

Multiregion sampling of de novo metastatic prostate cancer reveals complex polyclonality and augments clinical genotyping.

De novo metastatic prostate cancer is highly aggressive, but the paucity of routinely collected tissue has hindered genomic stratification and precision oncology. Here, we leveraged a rare study of surgical intervention in 43 de novo metastatic prostate cancers to assess somatic genotypes across 607 synchronous primary and metastatic tissue regions plus circulating tumor DNA. Intra-prostate heterogeneity was pervasive and impacted clinically relevant genes, resulting in discordant genotypes between select primary restricted regions and synchronous metastases. Additional complexity was driven by polyclonal metastatic seeding from phylogenetically related primary populations. When simulating clinical practice relying on a single tissue region, genomic heterogeneity plus variable tumor fraction across samples caused inaccurate genotyping of dominant disease; however, pooling extracted DNA from multiple biopsy cores before sequencing can rescue misassigned somatic genotypes. Our results define the relationship between synchronous treatment-sensitive primary and metastatic lesions in men with de novo metastatic prostate cancer and provide a framework for implementing genomics-guided patient management.

Resonance capture and resonance jump of the space debris with high area-to-mass ratio in the synchronous orbit region

Space debris near the synchronous orbit poses significant collision risks to spacecraft in this area. Therefore, it is necessary to analyze the orbital dynamics of space debris in order to predict its orbital evolution and prevent it from colliding with the spacecraft. Due to the combined effect of the dissipative forces and Earth’s 1:1 tesseral resonance, the space debris with high area-to-mass ratio near the synchronous orbit exhibits two special dynamical behaviors: resonance capture and resonance jump. By using a simplified model, this paper analyzes in detail the orbital evolution of the debris of the resonance capture and resonance jump, and explores the conditions for their occurrence. It is found that the dynamical behavior of space debris around the resonance capture or resonance jump is highly sensitive to its initial conditions. In addition, the long-term direct numerical integrations with the full dynamical model for the orbital evolution of the debris are performed. The difference between the phase space parameters of the resonance capture and resonance jump for space debris is discussed, and the pendulum-like oscillation of the resonant angle is also studied.

Vibration characteristic of free-to-rotate elliptical cylinder at low Reynolds number

Investigating the vibration characteristics of elliptical cylinders is important to harvest useful energy or suppress harmful vibration, but there still exist insufficiently understood in freely rotating elliptical cylinders. Herein, this paper investigates the transverse vibration characteristics of a freely rotating elliptical cylinder at Re = 150. The incompressible Navier-Stokes equation and structural dynamics equation are solved separately, and the two-way fluid-structure interaction is performed by exchanging fluid forces and structural displacements. The elliptical cylinder, with varying axial ratios (AR = 1.0–2.5) and mass ratios (m* = 10 or 5), can vibrate transversely and rotate around its center freely. The established numerical model is verified by the published results, and the numerical values are in good agreement with the experimental results. The vibration response and flow field characteristics over a range of reduced velocities (2 ≤ Ur ≤ 14) are explored. The results demonstrate that both the axial ratio and mass ratio significantly affect the vibration characteristics. Increasing the axial ratio or decreasing the mass ratio lead to a wider synchronization region. Within the synchronization region, the elliptical cylinder undergoes significant and unstable rotation, and P + S mode can be observed. Outside the synchronization region, only a small amplitude rotation takes place near the initial position, the transverse vibration amplitude is consistent with that of a non-rotatable elliptical cylinder, and the vortex shedding mode demonstrates 2S. This work provides important guidance in investigating the vibration characteristics of the elliptical cylinder.

Lyapunov exponents and extensivity of strongly coupled chaotic maps in regular graphs

In Thermodynamics and Statistical Physics, a system’s property is extensive when it grows with the system size. When it happens, the system can be decomposed into separate components, which has been done in many systems with weakly interacting components, such as for various gas models. Similarly, Ruelle conjectured 40 years ago that the Lyapunov exponents (LEs) of some sufficiently large chaotic systems are extensive, which led to study the extensivity properties of chaotic systems with strong interactions. Because of the complexities in these systems, most results achieved so far are restricted to numerical simulations. Here, we derive closed-form expressions for the LEs and entropy rate of coupled maps in finite- and infinite-sized regular graphs, according to the coupling strength, map’s chaoticity, and graph’s spectral properties. We show that this type of system has either 4 or 5 cases for the LEs, depending on the graph’s extreme Laplacian eigenvalues. These cases represent qualitatively different collective behaviours emerging in parameter space, including chaotic synchronisation (N−1 negative LEs) and incoherent chaos (N positive LEs). From the entropy rate, we show that the ring and complete graphs (nearest-neighbour and all-to-all couplings, respectively) are extensive in all parameter regions outside the chaotic synchronisation region. Although our derivations are restricted to one-dimensional maps with constant positive derivative (i.e., chaotic), our approach can be used to find LE and entropy rates for other regular graphs (such as for cyclic graphs) or be the basis for tackling small world graphs via perturbative methods.

Бифуркационный анализ области полной синхронизации системы неидентичных контактов Джозефсона

The structure of the region of complete synchronization of a system of three connected Josephson junctions, non-identical in critical currents, was studied by the method of bifurcation analysis. On the plane of non-identity parameters, lines of saddle-node bifurcations, Neumark-Sacker bifurcations and period doublings were found, corresponding to a typical synchronization region. The influence of symmetry on the structure of the region of complete synchronization has been studied. In the system, under certain conditions, pitchfork bifurcation and associated bistability are possible. Bogdanov-Takens points, cusp points and fold-flip points are also indicated. The accumulation of points of the latter type is discussed based on cycles of doubling periods near the boundary of the synchronization and chaos regions.

Cluster synchronization control for coupled genetic oscillator networks under denial-of-service attacks: Pinning partial impulsive strategy

This paper focuses on the security cluster synchronization (CS) of coupled genetic oscillator networks (GONs) with parameters mismatch under denial-of-service (DoS) attacks. Firstly, a model of DoS attacks on the control channel of GONs is established. Then, in order to achieve secure CS of GONs under DoS attacks, a pinning partial impulsive control (PPIC) strategy is proposed for the first time. Compared with the existing pinning impulsive control and partial impulsive control, the PPIC control method only controls part of the molecules of part of the genetic oscillators, so it has better performance in saving control cost. Moreover, we design an algorithm to obtain sufficient conditions for secure CS and the DoS attacks duration ratio that the system can tolerate. In addition, when the system is immune to DoS attacks, it can still achieve CS under PPIC. Finally, two numerical examples based on MATLAB software are presented to demonstrate the effectiveness of the results. The secure synchronization region is obtained, and the convergence efficiency of error systems under PPIC and pinning impulsive control is compared in the simulation.

Significant influence of fluid viscoelasticity on flow dynamics past an oscillating cylinder

This study focuses on numerically investigating the impact of fluid viscoelasticity on the flow dynamics around a transversely forced oscillating cylinder operating in the laminar vortex shedding regime at a fixed Reynolds number of $Re = 100$ . Specifically, we explore how fluid viscoelasticity affects the boundary between the lock-in and no lock-in regions and the corresponding wake characteristics compared with a simple Newtonian fluid. Our findings reveal that fluid viscoelasticity enables the synchronization of the vortex street with the cylinder motion at lower oscillation frequencies than those required for a Newtonian fluid. Consequently, the lock-in region boundary for a viscoelastic fluid differs from that of a Newtonian fluid and expands in the non-dimensional cylinder oscillation amplitude and frequency parameter space. In the primary synchronization region, the wake of a Newtonian fluid exhibits ‘2S’ (two single vortices) and ‘P+S’ (a pair of vortices and a single vortex) shedding modes. In contrast, a ‘2P’ (two pairs of vortices) vortex mode is observed for a viscoelastic fluid within the same region. To gain a deeper understanding of the differences in the coherent flow structures and their associated frequencies between the two fluids, we employ the data-driven reduced-order modelling technique, known as the dynamic mode decomposition (DMD) technique. Utilizing this technique, we successfully extract and visualize the two competing fundamental frequencies (cylinder oscillation and natural vortex shedding frequencies) and their associated flow structures in the case of the no lock-in state, whereas only the dominant cylinder oscillation frequency and associated flow structure in the case of the lock-in state. Furthermore, we propose that the presence of excess strain resulting from the stretching of polymer molecules in viscoelastic fluids leads to a distinct difference in the wake structure compared with Newtonian fluids. This observation aligns with the findings obtained from the $Q$ -criterion and vorticity transport analysis of the wake.

Transverse vortex-induced vibration of two elliptic cylinders in tandem: Effects of spacing

Renewable energy converters, such as bio-inspired fluttering foils, are gaining popularity due to their eco-friendly properties. However, the system with multiple objects has received scant attention. Here, we analyze how spacing influences the transverse (one-degree-of-freedom) vortex-induced vibration of two tandem identical elliptic cylinders at a constant Reynolds number by employing a wide range of reduced velocities (Ur∈[2,14]) and space ratios (L∗∈[2,6]). The incompressible Navier–Stokes equations are solved using the overset mesh method in the OpenFOAM® library. The findings indicate that the wake structure goes through eight distinct wake modes, as well as two gap flow patterns (reattachment and co-shedding). Vibrational responses, force parameters, and flow patterns determine three spacing configurations. At a small spacing (L∗=2), the upstream cylinder (UC) has the traditional lock-in (the frequency ratio fy/fn≃0.95–1.05) at the reduced velocity (Ur≃7), and the downstream cylinder (DC) has a narrow lock-in region around Ur≃9. However, the UC has a wide soft-lock-in (the synchronization region of fy/fn≃1.15) at high reduced velocities (Ur≃8–10). Here, the transverse vibrations of both cylinders, but especially the DC, reach relatively high amplitudes. At a moderate spacing (L∗=3), the UC bears a lock-in zone analogous to a single cylinder with the same mass ratio, while the DC shows a vast soft-lock-in zone (Ur≃8–14). At a large spacing (L∗=4, 5, and 6), the amplitude of the DC is often larger than that of a single cylinder when it is in the lock-in region. The DC exhibits a peak in amplitude at Ur = 7 and a wake-galloping region for Ur > 12.

Numerical simulation of flow past an 8:1 oscillating rectangular cylinder at Re = 22 000

To investigate the influence of structure’s oscillatory motion on flow, the present study employs the arbitrary Lagrangian–Eulerian method in k–ω shear stress transport (SST) turbulence model to simulate the flow past an oscillating rectangular cylinder at Re= 22 000. The cylinder undergoes reciprocating sinusoidal motion at a specified frequency f e, and the frequency ratio fr (defined as the ratio of cylinder oscillation frequency f e to the stationary cylinder vortex shedding frequency f 0), ranges from 0 to 4. The results demonstrate that, in the synchronization region (0.8 ⩽ fr⩽ 1.2), the drag coefficient shows the most notable variation and reaches its maxima at fr= 1.1 and the root mean square (r.m.s.) of the lift coefficient is proportional to the square of fr (, R 2 = 0.99). Moreover, the present study compares the similarities and differences of vortex shedding morphology between stationary and oscillating cylinders. With the increase of fr, the wake vortex gradually transforms from a single-row arrangement on the wake centerline to a parallel double-row arrangement, with the main vortex modes in the wake region observed as ‘2S’, ‘P + S’, ‘2P’ and ‘C’. Furthermore, spectral analysis, including amplitude spectrum analysis and wavelet analysis, in addition to probability density function statistical methods, are employed to comprehensively understand the velocity characteristics of the wake region. The results indicate that the oscillation of the cylinder reduces the correlation of the wake velocity. Those are beneficial in understanding the interaction between turbulence and structural fluid-induced motion.