Synchronization Dynamics Research Articles

Variation in synchrony of production among species, sites, and intertidal zones in coastal marshes.

Spatially synchronous population dynamics are important to ecosystem functioning and have several potential causes. By looking at synchrony in plant productivity over 18yr across two elevations in three types of coastal marsh habitat dominated by different clonal plant species in Georgia, USA, we were able to explore the importance of plant species and different habitat conditions to synchrony. Synchrony was highest when comparing within a plant species and within a marsh zone, and decreased across species, with increasing distance, and with increasing elevational differences. Abiotic conditions that were measured at individual sites (water column temperature and salinity) also showed high synchrony among sites, and in one case (salinity) decreased with increasing distance among sites. The Moran effect (synchronous abiotic conditions among sites) is the most plausible explanation for our findings. Decreased synchrony between creekbank and mid-marsh zones, and among habitat types (tidal fresh, brackish, and salt marsh) was likely due in part to different exposure to abiotic conditions and in part to variation in sensitivity of dominant plant species to these abiotic conditions. We found no evidence for asynchrony among species, sites or zones, indicating that one habitat type or zone will not compensate for poor production in another during years with low productivity; however, tidal fresh, brackish. and salt marsh sites were also not highly synchronous with each other, which will moderate productivity variation among years at the landscape level due to the portfolio effect. We identified the creekbank zone as more sensitive than the mid-marsh to abiotic variation and therefore as a priority for monitoring and management.

Kuramoto model with correlation between coupling strength and natural frequency

Abstract Synchronization is one of important collective behaviors in various systems. The identification of different synchronous dynamics and types of transition between different dynamical states has drawn great interests. In this work, we study Kuramoto model in the presence of correlation between coupling strength and natural frequency. By manipulating the correlation between coupling strength and natural frequency, synchronization transition can either be the continuous type or the discontinuous one. Rich synchronous dynamics and different transitions between them can be realized by manipulating the correlation. We hope that the coupled systems with correlation between coupling strength and natural frequency could provide a general platform to investigate synchronous dynamics.

Passive synchronization in optomechanical resonators coupled through an optical field

Abstract Synchronization in coupled optomechanical resonators has drawn a lot of concerns. In an experimental setup where two distant mechanical resonators interact with a common optical cavity field, synchronization between mechanical resonators has been reported [Phys. Rev. Lett. 111 (2013) 213902, ibid 124 (2020) 213902]. In this work, we numerically investigate the dynamical behaviors in such an experimental setup. We find synchronous dynamics as well as asynchronous dynamics such as chaotic behaviors. However, the synchronization between two mechanical resonators is not a collective dynamics but a passive one. In these synchronous states, one resonator is slaved by the other and the dominant resonator behaves like the one in a single optomechanical oscillator. There are two types of passive synchronous states depending on which resonator is the dominant one. These two types of synchronous states always coexist and which synchronous state is realized depends on initial conditions, which suggests that there is something elusive in the experimental setup to achieve synchronization collectively.

A MULTILEVEL RESOURCE-SAVING BLAST FURNACE PROCESS CONTROL

A multilevel resource-saving blast furnace process control is considered. The resource-saving control is provided for operating, adaptation, technical and economic control in the automated systems of blast-furnace processes. It is proposed to form optimal operation modes of blast furnace heating, metal charge structures, natural gas and oxygen consumption. Decisions are made using Kohonen neural networks taking into account current and planned parameters of coke quality, iron ore, raw materials and blast. At the level of operating control, the work suggests a model predictive control to improve the resource conservation indicators. The method is based on decomposition of the general problem of the process dynamics identification on particular problems: dynamic synchronization and identification of process transfer functions. At the level of adaptive control, optimal operating modes of blast furnaces are expedient to be developed with respect to blast furnace heating, structure of metal charge, natural gas and oxygen rate considering the current and planned parameters of coke, blasting. The blast furnace operating modes are suggested to be determined based on Kohonen neural networks. In evaluating the efficiency of introducing the model predictive control, the existing actual statistics of scatter of BF mode parameters should be based upon. The fact is that the introduction of model predictive control assumes no radical change of the BF melt technology. Like in all the control systems, the BF process is considered as the set control object with all its characteristics. Changing process settings, raw material content does not introduce any cardinal variation in the scatter of process characteristics. However, in this case a transient process occurs which is necessary for the control system to identify the changing conditions. The transient process is inherent to all the control systems and the blast furnace process is not an exclusion. As a result of transient process, the control system is set to the optimal mode.

Modeling Cell Energy Metabolism as Weighted Networks of Non-autonomous Oscillators.

Networks of oscillating processes are a common occurrence in living systems. This is as true as anywhere in the energy metabolism of individual cells. Exchanges of molecules and common regulation operate throughout the metabolic processes of glycolysis and oxidative phosphorylation, making the consideration of each of these as a network a natural step. Oscillations are similarly ubiquitous within these processes, and the frequencies of these oscillations are never truly constant. These features make this system an ideal example with which to discuss an alternative approach to modeling living systems, which focuses on their thermodynamically open, oscillating, non-linear and non-autonomous nature. We implement this approach in developing a model of non-autonomous Kuramoto oscillators in two all-to-all weighted networks coupled to one another, and themselves driven by non-autonomous oscillators. Each component represents a metabolic process, the networks acting as the glycolytic and oxidative phosphorylative processes, and the drivers as glucose and oxygen supply. We analyse the effect of these features on the synchronization dynamics within the model, and present a comparison between this model, experimental data on the glycolysis of HeLa cells, and a comparatively mainstream model of this experiment. In the former, we find that the introduction of oscillator networks significantly increases the proportion of the model's parameter space that features some form of synchronization, indicating a greater ability of the processes to resist external perturbations, a crucial behavior in biological settings. For the latter, we analyse the oscillations of the experiment, finding a characteristic frequency of 0.01–0.02 Hz. We further demonstrate that an output of the model comparable to the measurements of the experiment oscillates in a manner similar to the measured data, achieving this with fewer parameters and greater flexibility than the comparable model.

Dynamic Uni- and Multicellular Patterns Encode Biphasic Activity in Pancreatic Islets.

Biphasic secretion is an autonomous feature of many endocrine micro-organs to fulfill physiological demands. The biphasic activity of islet β-cells maintains glucose homeostasis and is altered in type 2 diabetes. Nevertheless, underlying cellular or multicellular functional organizations are only partially understood. High-resolution noninvasive multielectrode array recordings permit simultaneous analysis of recruitment, of single-cell, and of coupling activity within entire islets in long-time experiments. Using this unbiased approach, we addressed the organizational modes of both first and second phase in mouse and human islets under physiological and pathophysiological conditions. Our data provide a new uni- and multicellular model of islet β-cell activation: during the first phase, small but highly active β-cell clusters are dominant, whereas during the second phase, electrical coupling generates large functional clusters via multicellular slow potentials to favor an economic sustained activity. Postprandial levels of glucagon-like peptide 1 favor coupling only in the second phase, whereas aging and glucotoxicity alter coupled activity in both phases. In summary, biphasic activity is encoded upstream of vesicle pools at the micro-organ level by multicellular electrical signals and their dynamic synchronization between β-cells. The profound alteration of the electrical organization of islets in pathophysiological conditions may contribute to functional deficits in type 2 diabetes.

Stochastic synchronization of dynamics on the human connectome

Synchronization is a collective mechanism by which oscillatory networks achieve their functions. Factors driving synchronization include the network’s topological and dynamical properties. However, how these factors drive the emergence of synchronization in the presence of potentially disruptive external inputs like stochastic perturbations is not well understood, particularly for real-world systems such as the human brain. Here, we aim to systematically address this problem using a large-scale model of the human brain network (i.e., the human connectome). The results show that the model can produce complex synchronization patterns transitioning between incoherent and coherent states. When nodes in the network are coupled at some critical strength, a counterintuitive phenomenon emerges where the addition of noise increases the synchronization of global and local dynamics, with structural hub nodes benefiting the most. This stochastic synchronization effect is found to be driven by the intrinsic hierarchy of neural timescales of the brain and the heterogeneous complex topology of the connectome. Moreover, the effect coincides with clustering of node phases and node frequencies and strengthening of the functional connectivity of some of the connectome’s subnetworks. Overall, the work provides broad theoretical insights into the emergence and mechanisms of stochastic synchronization, highlighting its putative contribution in achieving network integration underpinning brain function.

Cardiac Muscle Cell‐Based Coupled Oscillator Network for Collective Computing

Current rate of data generation and the need for real‐time data analytics can benefit from new computational approaches where computation proceeds in a massively parallel way while being scalable and energy efficient. Biological systems arising from interaction of living cells can provide such pathways for sustainable computing. Current designs for biocomputing leveraging the information processing units of the cells, such as DNA, gene, or protein circuitries, are inherently slow (hours to days speed) and, therefore, are primarily being considered for archival storage of information. On the contrary, electrically active cells that can synchronize in milliseconds and can be connected as networks to perform massively parallel tasks can transform biocomputing and lead to novel ways of high throughput information processing. Herein, coupled oscillator networks made of living cardiac muscle cells, or bio‐oscillators, is explored as collective computing components for solving computationally hard problems. An empirically validated circuit compatible macromodel is developed for the bio‐oscillators and the fibroblast cells acting as coupling elements, to faithfully reproduce the synchronization dynamics of the network and it is shown that such bio‐oscillator network can be scaled up to hundreds of nodes and be used to solve computationally hard problems faster than traditional heuristics‐based Boolean algorithms.

ECONOMETRIC ANALYSIS OF INDICATORS OF DEVELOPMENT OF FINANCIAL AND REAL ECONOMIC SECTORS

The instability of the domestic economy and the influence of external factors lead to the deviation of the basic macroeconomic indicators from the normative equilibrium values. This requires the development of a qualitatively new integrated approach to the analysis of the main macroeconomic indicators of the development of the economy sectors in order to identify the effective institutional and financial foundations for stimulating economic progress of our state.
 The purpose of the work is to study the theoretical positions of the financial and real sectors of the economy and conduct an econometric analysis of the indicators of their development.
 Results. Theoretical positions about the place of the real and financial sectors of the economy in the general economic system of the state has been systematized in the article. The main indicators (KPIs — key performance indicators) of the studied sectors of the economy has been revealed. The econometric analysis of the main indicators of the development of the economy sectors has been based on real (actual) values corrected for inflation and has been presented in the classical theoretical Hix-Hansen equilibrium model on commodity and money markets (IS-LM).
 The data of the National Bank of Ukraine on the dynamics of the monetary base (B) and monetary aggregates (M0 — M3), and the State Statistics Service of Ukraine on GDP (Y) and inflation (СРІ) has been used in the research. The econometric analysis has showed a significant correlation between the nominal and real GDP, money supply and money base indicators, which are almost synchronized during 2001—2017. The presence of strong interdependence between the real values of these indicators has been confirmed by very high correlation values, which are ranged from 0.94 to 0.99. Almost functional dependence of the money supply on the monetary base has been explained by the availability of the existing mechanism of monetary multiplication, and the money market multiplier tends to increase. The high statistical dependence between the real NBU discount rate and the weighted average rate on all instruments has been revealed. It proved the effectiveness of the main instrument for implementing the discrete monetary policy of macroeconomic regulation. The negative significance of the correlation coefficients between the interest rates and the quantitative indicators of the real and financial sectors of the economy has shown that the traditional theoretical compromise in choosing the main problems to be solved in the economy to ensure macroeconomic stability is also typical for Ukraine. The application of the «expensive money» policy to combat high inflation negatively affects the real money supply, but taking into account the very high dependence between it and GDP, slows down the growth of the real sector of the economy, and vice versa.
 The obtained two-factor regression equation with very high reliability has explained by the retrospective changes in the real money supply. The most important factor for it is real GDP. This confirms the strong interconnection between the real and financial sectors of the economy in the process of developing the economic system. Quantitative indicators of development of both sectors are under the influence of long-term trends. They have their own nature and often depend on trends in the development of the world economy and finance as well as internal problems that are often predictable.
 Conclusions. The results has been obtained suggest that the synchronous long-term dynamics of real GDP, money supply and money base, as well as the statistical interdependence between them, firstly, signal that in Ukraine the rules of a market economy have already been formed and can be applied effectively in such conditions of the methods and tools of macroeconomic regulation, and secondly, processes occurring in one of the specified sectors of the economy will necessarily reflect on another. Therefore, solving macroeconomic problems requires a balanced and integrated approach taking into account the nature and strength of the interdependence between different processes and phenomena.

Dynamics of topological defects and structural synchronization in a forming periodic tissue

Living organisms form a large variety of hierarchically structured extracellular functional tissues. Remarkably, these materials exhibit regularity and structural coherence across multiple length scales, far beyond the size of a single cell. Here, synchrotron-based nanotomographic imaging in combination with machine-learning-based segmentation is used to reveal the structural synchronization process of nacre forming in the shell of the mollusc Unio pictorum. We show that the emergence of this highly regular layered structure is driven by a disorder-to-order transition achieved through the motion and interaction of screw-like structural dislocations with an opposite topological sign. Using an analogy to similar processes observed in liquid-crystalline systems, we demonstrate that these microstructural faults act as dissipative topological defects coupled by an elastic distortion field surrounding their cores. Their mutual annihilation results in structural synchronization that is simulated using the classical Kuramoto model. The developed experimental, theoretical and numerical framework provides a comprehensive physical view of the formation of biogenic materials. Molluscs assemble layers of material in the shells around them with a high level of control. Here the authors observe the structural evolution of layer formation and propose a mechanism reminiscent of topological defect dynamics in liquid crystals.

Transient Damping Method for Improving the Synchronization Stability of Virtual Synchronous Generators

The virtual synchronous generator (VSG) was proposed to emulate a synchronous machine's dynamics when integrating power electronic converter-based distributed energy resources to the power grid. However, the VSG's synchronization stability during grid faults is not fully explored. The underlying mechanism of loss of synchronization still needs to be further revealed due to VSG's nonlinear characteristics. In this article, a step-by-step analytical method based on combining the linear and nonlinear models is proposed to analyze VSG's dynamic behaviors during a large disturbance. The relationship between the linear and nonlinear models is first brought to light, showing that the linear model is suitable for qualitative analysis to give an intuitive physical insight. Simultaneously, the latter is adopted for quantitative analysis to assess stability after a grid fault. Moreover, to avoid the conflict of the synchronization stability and the inertia response, a transient damping method is added in the active power control loop, which can simultaneously improve the synchronization stability and frequency stability. Design guidelines are also proposed to identify the parameter of the transient damping with different inertia requirements. Finally, the experimental results verify the analytical method and the theoretical analysis.

Synthetic Inertia Control of Grid-connected Inverter Considering the Synchronization Dynamics

The increasing penetration of renewable energy resources facilitates the carbon footprint reduction process yet reduces the power system inertia. As a result, the grid frequency and the rate of change of frequency (RoCoF) might probably go beyond the normal range, resulting in unexpected load shedding, generator tripping, and even frequency instability. To address this problem, grid-connected inverters are designed to participate in frequency regulation and provide the equivalent inertial support. Nevertheless, the inertia emulation effect is affected by the inverter synchronization dynamic and high RoCoF events may occur as the result of poor synchronization dynamics. In view of this limitation, a synthetic inertia control is developed in this article considering the synchronization dynamics. The synthetic inertia principles and control design guideline are explicitly provided. Finally, hardware experimental results of a scaled-down power system prototype are provided to validate the effectiveness of the proposed approach.

Resistive force theory and wave dynamics in swimming flagellar apparatus isolated from C. reinhardtii.

Cilia-driven motility and fluid transport are ubiquitous in nature and essential for many biological processes, including swimming of eukaryotic unicellular organisms, mucus transport in airway apparatus or fluid flow in the brain. The-biflagellated micro-swimmer Chlamydomonas reinhardtii is a model organism to study the dynamics of flagellar synchronization. Hydrodynamic interactions, intracellular mechanical coupling or cell body rocking is believed to play a crucial role in the synchronization of flagellar beating in green algae. Here, we use freely swimming intact flagellar apparatus isolated from a wall-less strain of Chlamydomonas to investigate wave dynamics. Our analysis on phase coordinates shows that when the frequency difference between the flagella is high (10–41% of the mean), neither mechanical coupling via basal body nor hydrodynamics interactions are strong enough to synchronize two flagella, indicating that the beating frequency is perhaps controlled internally by the cell. We also examined the validity of resistive force theory for a flagellar apparatus swimming freely in the vicinity of a substrate and found quantitative agreement between the experimental data and simulations with a drag anisotropy of ratio 2. Finally, using a simplified wave form, we investigated the influence of phase and frequency differences, intrinsic curvature and wave amplitude on the swimming trajectory of flagellar apparatus. Our analysis shows that by controlling the phase or frequency differences between two flagella, steering can occur.

Reconfigurable FPGA Realization of Fractional-Order Chaotic Systems

This paper proposes FPGA realization of an IP core for generic fractional-order derivative based on Grünwald-Letnikov approximation. This generic design is applied to achieve reconfigurable realization of fractional-order chaotic systems. The fractional-order real-time configuration boosts the suitability of this particular realization for different applications, including dynamic switching, synchronization, and encryption. The proposed design targets optimized utilization of the FPGA internal resources and efficient employment of the external peripherals: switches and I/O ports in the FPGA board. The digital design of the fractional-order dependent terms: binomial coefficients and power function is proposed. Three approximations of the power function using curve fitting are compared, settling on the quadratic approximation that balances accuracy and efficiency. Three fractional-order chaotic systems: Liu, Li and Chen four-wing, are verified for both commensurate and incommensurate orders cases, using one approach for the commensurate order case and two approaches for the incommensurate order case. The reconfigurable design is realized on the Artix-7 FPGA board, yielding throughputs of 1.1266, 1.1266, and 1.434 Gbit/s for both commensurate and incommensurate orders cases of the three systems, respectively. Compared to recent related works, the proposed implementation demonstrates its efficient hardware utilization and suitability for potential applications.

Dynamical distributed control and synchronization

It is well known that most of real-world phenomena are described by partial differential equations. Nevertheless, for control design purposes it is very common to approximate them with a set of ordinary differential equations, since conventional design methods, such as calculus of variations or differential geometry, turn out to be very complex for this class of systems. However, by doing this, valuable properties are lost. In this work, we present a dynamical distributed control for nonlinear partial differential equation systems and we focus on solving the Generalized Synchronization problem, since this topic has multiple applications in the disciplines of engineering, biology, physics, etc. For the design of the control, we utilize a differential algebraic approach. The key ingredient of our design method is to find a canonical form of the given systems by means of the so-called partial differential primitive element. This representation is known as Generalized Observability Canonical Form and allows us to design a dynamical distributed control in a natural way. Additionally, to avoid a functional analysis for the stability of the resultant synchronization error, we propose to utilize tools from semi-group and spectral theory of infinite dimensional systems in a Hilbert space. As a result, we present a design approach less complex and, therefore, more accessible than most common design methods. Besides, with the proposed stability analysis, we obtain an easy criterion to select the control gains; hence, we can solve the generalized synchronization problem of partial differential equation systems in a simple way. To validate the effectiveness of the proposed control, we present two examples of generalized synchronization for reaction-diffusion systems and show their respective numerical results.

Neurophysiological Characteristics of Competition in Skills and Cooperation in Creativity Task Performance: A Review of Hyperscanning Research

The review considers the studies of neurophysiological indices of human brain activity in different types of joint actions. The results of studies were summarized to describe the neurophysiological correlates of joint performance of creative or artistic (musical) tasks by several subjects simultaneously in conditions of cooperation or competition. Involvement in joint activities presumably causes the neurophysiological rearrangements of human brain activity that are not observed during tasks performed individually, but characterize the situations of interactions between subjects. The nature of interactions (competition or cooperation) essentially affects brain activity. Interbrain synchronization has been found to increase during cooperation and decrease in conditions that do not require interactions. In performing arts (music improvisation), the performers’ coordinated activity, which can be considered as cooperation, evokes a dynamic interbrain synchronization pattern in frontal and central cortical areas mainly in low-frequency (Δ and θ) EEG bands. Functional near-infrared spectroscopy (fNIRS) has shown that cooperation in performing creativity tasks is characterized by an increase of inter-subject synchronization of the prefrontal, temporal, and temporal-parietal areas of the left and right hemispheres, while no inter-subject synchronization has been observed in competitive contexts.

Fuzzy remodeling and synchronization of nonlinear systems

Synchronization is one of the crucial control problems in coordinated behavior systems. A wide range of applications necessitates the development and improvement of approaches to solving the linearization problem for non-linear systems with complex behavior. Hence the paper offers an approach to solving the problem of chaotic system coordinate synchronization based on the use of fuzzy remodeling and superstability conditions. It is shown that transition from general (non-linear) synchronization problem statement to fuzzy description with fuzzy Takagi-Sugeno models allows transforming the initial task to a well understood problem of fuzzy T-S system stabilization that describes the dynamics synchronization error. As a candidate solution for the problem we offer a way of implementing superstability conditions that reduce the task of finding fuzzy regulator to solving a linear programming task. It is shown that implementation of superstability conditions not only presents a simple way of solving the problem, but also has practical value. Superstability provides the monotonesness of the transient process of synchronization without sharp spikes of solution norm. The efficiency of the offered approach is demonstrated by the example of synchronization of two hyperchaotic systems. To prove the efficiency of superstability conditions the solution of the robust synchronization problem with parametric uncertainty in system matrices is given. The presented results can be applied for synchronization of various nonlinear systems demonstrating chaotic dynamics.

The Use of Artificial Intelligence‐Based Optical Remote Sensing and Positioning Technology in Microelectronic Processing Technology

The purpose is to make defect detection in microelectronic processing technology fast, accurate, reliable, and efficient. A new optical remote sensing‐optical beam induced resistance change (ORS‐OBIRCH) target recognition and location defect detection method is proposed based on an artificial intelligence algorithm, optical remote sensing (ORS), and optical beam induced resistance change (OBIRCH) location technology using deep convolutional neural network. This method integrates the characteristics of high resolution and rich details of the image obtained by ORS technology and combines the advantages of photosensitive temperature characteristics in OBIRCH positioning technology. It can be adopted to identify, capture, and locate the defects of microdevices in the process of microelectronic processing. Simulation results show that this method can quickly reduce the detection range and locate defects accurately and efficiently. The experimental results reveal that the ORS‐OBIRCH target recognition defect location detection method can complete the dynamic synchronization of the IC detection system and obtain high‐quality images by changing the laser beam irradiation cycle. Moreover, it can analyze and process the detection results to quickly, accurately, and efficiently locate the defect location. Unlike the traditional detection methods, the success rate of detection has been greatly improved, which is about 95.8%, an increase of nearly 40%; the detection time has been reduced by more than half, from 5.5 days to 1.9 days, and the improvement rate has reached more than 65%. In a word, this method has good practical application value in the field of microelectronic processing.

Chaos-control and parallel queue synchronization of laser local area network

In this work, we study the chaos-control and parallel queue synchronization of a laser local area network (LAN). We present and study specifically a “single-queue-double-parameter” method of the parallel series queue dynamic behavior synchronization of the controlled laser LAN under two optoelectronic delay feedback controllers, and establish the mathematical and physical model of the controlled laser LAN. The LAN node is composed of two space coupled lasers with different parameters and other two single lasers, where two lasers series produce two different parallel queues, which results in two different chains of LAN nodes. Optical LAN links are composed of two optical parallel-crossing paths and two photoelectric delay feedback controllers setting in two lasers of LAN, which creates a method of double-parameter control of LAN. Through the analysis of the stability theory of differential equation and the dynamic characteristic equation of coupled lasers of LAN, our mathematical theory demonstrates that the chaos-control of laser LAN can be achieved by two photoelectric delay feedback controllers adjusting photoelectric feedback levels and feedback delay time of one of the two coupled laser and another single laser, respectively. Making analysis of the stability theory of differential equation and the dynamic characteristic equation of LAN nodes in two queue chains, we demonstrate theoretically how to obtain synchronization in network nodes of the controlled LAN on two queue chains by controlling optical feedback levels, and by the photoelectric delay feedback controllers adjusting photoelectric feedback levels and feedback delay time, respectively. Using our numerical calculation of parallel queue synchronization, the node laser’s waveform and its phase space trajectory, we find that very lasers of network nodes of the controlled LAN can lead to the parallel queue synchronization of a double-period, a three-period, a four-period and other quasi-periods while these quasi-periodic synchronizations and dynamic synchronizations are controlled in two queue chains of LAN nodes when we let the photoelectric feedback level and the delay time shift on some parameters. We find also two controlled quasi-periodic parallel queue synchronization regions. This paper also presents an application case of laser LAN multi-point chaotic carrier synchronous emission and ultra-wideband communication. This is a new type of controlled laser LAN system, which has the core elements of optical LAN and the characteristics of multi-variable, multi-dimension and parallel queue chaos-control techniques of complex dynamic networks. It also has the function of optical network ultra-wideband communication. The results have important reference value for studying the LAN, optical network and its synchronization and control, laser technology and chaos.

Synchronization Dynamics in Non-Normal Networks: The Trade-Off for Optimality.

Synchronization is an important behavior that characterizes many natural and human made systems that are composed by several interacting units. It can be found in a broad spectrum of applications, ranging from neuroscience to power-grids, to mention a few. Such systems synchronize because of the complex set of coupling they exhibit, with the latter being modeled by complex networks. The dynamical behavior of the system and the topology of the underlying network are strongly intertwined, raising the question of the optimal architecture that makes synchronization robust. The Master Stability Function (MSF) has been proposed and extensively studied as a generic framework for tackling synchronization problems. Using this method, it has been shown that, for a class of models, synchronization in strongly directed networks is robust to external perturbations. Recent findings indicate that many real-world networks are strongly directed, being potential candidates for optimal synchronization. Moreover, many empirical networks are also strongly non-normal. Inspired by this latter fact in this work, we address the role of the non-normality in the synchronization dynamics by pointing out that standard techniques, such as the MSF, may fail to predict the stability of synchronized states. We demonstrate that, due to a transient growth that is induced by the structure’s non-normality, the system might lose synchronization, contrary to the spectral prediction. These results lead to a trade-off between non-normality and directedness that should be properly considered when designing an optimal network, enhancing the robustness of synchronization.