Synchronization Of Networks Research Articles

Distributed delayed impulsive control for [formula omitted]-synchronization of multi-link structure networks with bounded uncertainties and time-varying delays of unmeasured bounds: A novel Halanay impulsive inequality approach

This study discusses the μ−synchronization of multi-link structure networks with parameter uncertainties and nonlinear couplings. Three types of variable delays, including internal, coupling, and distributed delays at sampling moments are deliberated in the synchronization control process. Different from existing multi-link models, the bulk of delays can be non-differentiable and unmeasured, which also brings new challenges to our research. To conquer the difficulties caused by such multiple generalized time delays, a novel Halanay-like impulsive inequality is established by utilizing the properties of μ−function and mathematical induction recipes. For letting the multi-link networks achieve μ−synchronization, a distributed-delay impulsive controller is designed, and multiple coupling matrices are decomposed into diagonal matrices and residual matrices. Based on the stability function method, the derived impulsive inequality, and matrix decomposition techniques, important synchronization conditions for the concerning multi-link networks are obtained, which releases the traditional constraints that delays should be smaller than impulsive intervals, and popularizes the existing synchronization results respecting multi-link systems with unbounded delays.

Further on Pinning Synchronization of Dynamical Networks with Coupling Delay

Further on Pinning Synchronization of Dynamical Networks with Coupling Delay

Finite-time synchronization of fractional-order uncertain quaternion-valued neural networks via slide mode control

This paper investigates finite-time synchronization of fractional-order quaternion-valued neural networks (F-QV-NNs), involving uncertainties in the system parameters. We adopt a combined approach of sliding mode control (SMC) and a non-separation strategy to achieve finite-time synchronization. Based on SMC theory, we construct a specific sliding surface and design a controller to ensure the occurrence of sliding motion. To achieve the desired sliding motion, we apply the fractional Lyapunov direct method to guide the system's states to the designed sliding surface. Moreover, the derived sufficient conditions ensure finite-time synchronization within the models. Lastly, we give a numerical example to validate the effectiveness of the acquired results.

Investigating the spatial propagation patterns of meteorological drought events and underlying mechanisms using complex network theory: A case study of the Yangtze River Basin, China

The spatial propagation patterns of meteorological drought events (MDEs) and underlying mechanisms contribute to elucidating and forecasting drought evolution. In this study, gridded MDEs in the Yangtze River Basin (YRB) throughout the entire year, wet season and dry season were extracted from 3-month Standardized Precipitation Evapotranspiration Index (SPEI-3) series. Event synchronization (ES) and complex networks (CN) were employed to construct the MDE synchronization networks and MDE spatial propagation networks for various periods. The former were utilized to identify MDE synchronized subregions where MDEs co-occur and co-evolve in the YRB, while the latter were used to quantify the MDE spatial propagation patterns over both the basin and its subregions. The driving mechanisms behind MDE spatial propagation were further investigated by diagnosing the concomitant drought-inducing climate systems. The findings reveal the presence of four MDE synchronized subregions during the wet season and five subregions during the entire year and dry season. These subregions exhibited distinct spatial propagation patterns of MDEs, aligning with overall findings across the YRB. Notable differences were observed between wet and dry seasons, with various subregions exhibiting distinctive spatial propagation patterns during each season. These patterns are driven by variations in the controlling atmospheric circulation systems, leading to anomalies of wind patterns and moisture distribution, ultimately resulting in deficient moisture supply. The variations of tropical sea surface thermal conditions, influences of the Tibetan Plateau and MDE self-propagation triggered by land–atmosphere feedback are considered as three primary influencing factors for MDE spatial propagation in the YRB.

Dynamics of synchronous Boolean networks with non-binary states.

In this paper, we study the dynamics of synchronous Boolean networks and extend previously obtained results for binary Boolean networks to networks with state variables in a general Boolean algebra of 2p elements, with p>1. The method to do this is based on the Stone representation theorem and the relation of such systems on general Boolean algebras with those with binary-state values. Specifically, we deal with the main periodic orbit problems and predecessor problems (existence, coexistence, uniqueness, and number of them), which allows us to determine the periodic structure and the attractor cycles of the system. These results open opportunities to explore novel applications by means of such general systems.

Scalable synchronization cluster in networked chaotic oscillators.

Cluster synchronization in synthetic networks of coupled chaotic oscillators is investigated. It is found that despite the asymmetric nature of the network structure, a subset of the oscillators can be synchronized as a cluster while the other oscillators remain desynchronized. Interestingly, with the increase in the coupling strength, the cluster is expanding gradually by recruiting the desynchronized oscillators one by one. This new synchronization phenomenon, which is named "scalable synchronization cluster," is explored theoretically by the method of eigenvector-based analysis, and it is revealed that the scalability of the cluster is attributed to the unique feature of the eigenvectors of the network coupling matrix. The transient dynamics of the cluster in response to random perturbations are also studied, and it is shown that in restoring to the synchronization state, oscillators inside the cluster are stabilized in sequence, illustrating again the hierarchy of the oscillators. The findings shed new light on the collective behaviors of networked chaotic oscillators and are helpful for the design of real-world networks where scalable synchronization clusters are concerned.

Reinforcement learning-based pinning control for synchronization suppression in complex networks

Synchronization in complex networks is a ubiquitous and important phenomenon with implications in various fields. Excessive synchronization may lead to undesired consequences, making desynchronization techniques essential. Exploiting the Proximal Policy Optimization algorithm, this work studies reinforcement learning-based pinning control strategies for synchronization suppression in global coupling networks and two types of irregular coupling networks: the Watts-Strogatz small-world networks and the Barabási-Albert scale-free networks. We investigate the impact of the ratio of controlled nodes and the role of key nodes selected by the LeaderRank algorithm on the performance of synchronization suppression. Numerical results demonstrate the effectiveness of the reinforcement learning-based pinning control strategy in different coupling schemes of the complex networks, revealing a critical ratio of the pinned nodes and the superior performance of a newly proposed hybrid pinning strategy. The results provide valuable insights for suppressing and optimizing network synchronization behavior efficiently.

Finite/fixed-time cluster synchronization for directed and multiplex coupled dynamic networks

This article deals with finite/fixed-time cluster synchronization (FnTCS/FdTCS) issue for directed and multiplex coupled dynamic networks (MCDNs). Finite/fixed-time synchronization of multiplex networks has become a popular research topic, which indicates that, state information is utilized for synchronization, and the settling time depends on original condition for a range of finite time, while the time is bounded with arbitrary original value for fixed-time one. Through constructing appropriate feedback control protocol, FnTCS and FdTCS matters for MCDNs are settled under re-arranging variables' order technique. The present model contains the case that outer matrices (OMs) can be directed, with competitive elements, and not even connected, while previous and related researches assumed that OMs were undirected, cooperative and connected, so existing results can be improved for more general and broader regulations. This strategy above is presented to solve directed CDNs with multiweights from angle of inner and outer matrices, and we prove that if the weighted group of added OMs for each dimension is strongly connected, then cluster synchronization rules are established in finite/fixed time. Moreover, we also earn finite/fixed-time synchronization criteria when the cluster is single. In addition, the issue of FnTCS/FdTCS is developed for directed and multiplex coupled reaction-diffusion networks (MCRDNs) as an application. The validity of these gained results is verified by simulated examples.

Towards a Classification of Steady-State Bifurcations for Networks with Asymmetric Inputs

We consider homogeneous coupled cell networks with asymmetric inputs. We obtain general results concerning codimension-one steady-state bifurcations for networks with any number of cells and any number of asymmetric inputs. These results rely solely on the network adjacency matrices eigenvalue structure and the existence, or not, of network synchrony subspaces. For networks with three cells, we describe the possible lattices of synchrony subspaces annotated with the eigenvalues on each synchrony subspace. Applying the previous results, we classify the synchrony-breaking steady-state bifurcations that can occur for three-cell minimal networks with one, two or six asymmetric inputs.

Brain Connectivity Dynamics and Mittag–Leffler Synchronization in Asymmetric Complex Networks for a Class of Coupled Nonlinear Fractional-Order Memristive Neural Network System with Coupling Boundary Conditions

This paper investigates the long-time behavior of fractional-order complex memristive neural networks in order to analyze the synchronization of both anatomical and functional brain networks, for predicting therapy response, and ensuring safe diagnostic and treatments of neurological disorder (such as epilepsy, Alzheimer’s disease, or Parkinson’s disease). A new mathematical brain connectivity model, taking into account the memory characteristics of neurons and their past history, the heterogeneity of brain tissue, and the local anisotropy of cell diffusion, is proposed. This developed model, which depends on topology, interactions, and local dynamics, is a set of coupled nonlinear Caputo fractional reaction–diffusion equations, in the shape of a fractional-order ODE coupled with a set of time fractional-order PDEs, interacting via an asymmetric complex network. In order to introduce into the model the connection structure between neurons (or brain regions), the graph theory, in which the discrete Laplacian matrix of the communication graph plays a fundamental role, is considered. The existence of an absorbing set in state spaces for system is discussed, and then the dissipative dynamics result, with absorbing sets, is proved. Finally, some Mittag–Leffler synchronization results are established for this complex memristive neural network under certain threshold values of coupling forces, memristive weight coefficients, and diffusion coefficients.

Exponential Synchronization of Coupled Neural Networks with Hybrid Delays and Stochastic Distributed Delayed Impulses

Exponential Synchronization of Coupled Neural Networks with Hybrid Delays and Stochastic Distributed Delayed Impulses

Fixed/Prescribed-time synchronization of multi-layer complex networks under switching control

The fixed/preassigned time (FT/PT) synchronization issue of multi-layer networks via a discontinuous control strategy is addressed in this paper. Firstly, the inventiveness FT theorem is established, and a precise estimation of setting time is given by employing mathematical induction, proof by contradiction, and maximum value theory. Subsequently, based on the FT stability results, several FT synchronization criteria for multi-layer networks are proposed by designing a periodically switching protocol. Additionally, the topological connectivity constraints are eliminated through the implementation of synchronized states as virtual nodes. Correspondingly, the PT synchronization issue is investigated by developing several extraordinary control strategies in which the control gains are finite. Ultimately, the feasibility of the developed control design and the established criteria is illustrated by two numerical examples.

Sampled‐data‐based synchronization of complex networks under scaling attacks

In this study, our main objective is to address the issue of sampled‐data‐based synchronization of complex networks subjected to stochastic scaling attacks using a looped‐functional approach. To begin with, the design of a Lyapunov functional, which involves tuning parameters and slack variables, considers the error state information of and . Then, the scaling attack is a type of deception attack that is formulated using an interval matrix approach. In addition, the complex networks considered in this study incorporate uncertain inner coupling strengths, which are more general than the existing ones, owing to the presence of uncertainties in the coupling strengths. Using a looped‐functional approach to construct an appropriate Lyapunov–Krasovskii functional, we derive a set of sufficient conditions to achieve mean‐square asymptotic synchronization for considered complex networks under scaling attacks. In the end, the proposed results are illustrated using three examples, including a practical example that highlights their effectiveness and superiority.

Synchronization for uncertain neural networks with randomly occurring uncertainties and time-delay based on the sliding mode control

Synchronization for uncertain neural networks with randomly occurring uncertainties and time-delay based on the sliding mode control

Quasi-projective synchronization of non-identical time-varying delayed quaternion-valued neural networks with interaction terms: Direct method

This article investigates the quasi-projective synchronization (QPS) of non-identical quaternion-valued neural networks (QVNNs) with time-varying delays and interaction terms. Due to parameter mismatches between the drive and response systems, complete projective synchronization is not possible. As a result, a novel idea, known as QPS, is explored up to a small error bound. The direct method is used to derive several general criteria to achieve QPS. The Lyapunov stability theory is employed to estimate the error bound. The numerical simulation results are presented graphically for various special cases to demonstrate the synchronization of time-varying delayed QVNNs with mismatched parameters and interaction terms, which confirm the efficiency of the presented research results. The second example showcases the application of QVNNs coupled with associative memory to illustrate its efficacy in accurately restoring the original color image patterns.

Exponential synchronization of dynamical complex networks via random impulsive scheme

This paper investigates the synchronization of a complex network based on a class of random impulsive differential equation systems. Based on the random impulsive strategy of Poisson distribution, a random impulsive dynamical network model is constructed. Using the Lyapunov principle, random process theory, linear matrix inequality method, and some basic analysis methods, we realize the global mean-square index synchronization of the model. We then get sufficient criteria for the synchronization. By presenting a numerical example, we verified the validity of the theoretical results.

Strategic integration of vertiport planning in multimodal transportation for urban air mobility: A case study in Beijing, China

In pursuit of strategic sustainable development goals, this study seeks to analyze the spatial placement of vertiports for urban air mobility, positioning them as integral components within the multimodal transportation system. We propose an iterative weighted k-means clustering method that incorporates the value of travel time of different transportation modes to identify potential vertiport locations. A multi-objective optimization model that maximizes total air taxi ridership and minimizes total facility costs and travel distances to vertiports is developed considering the constraints of the distance from vertiports to existing mobility hubs. A case study is conducted using the data of Beijing city, incorporating the modes of taxis and metro. We found that 19 vertiports can guarantee a robust performance of urban air mobility service. Users of urban air mobility can benefit from substantial travel time savings of 80% (48 min on average). This study contributes to a deeper understanding of the optimal setting of urban air mobility facilities from the perspective of network synchronization, offering useful insights into policy decision-making for sustainable infrastructure planning.

Modeling mTORopathy-related epilepsy in cultured murine hippocampal neurons using the multi-electrode array

The mechanistic target of rapamycin complex 1 (mTORC1) signaling pathway is a ubiquitous cellular pathway. mTORopathies, a group of disorders characterized by hyperactivity of the mTORC1 pathway, illustrate the prominent role of the mTOR pathway in disease pathology, often profoundly affecting the central nervous system. One of the most debilitating symptoms of mTORopathies is drug-resistant epilepsy, emphasizing the urgent need for a deeper understanding of disease mechanisms to develop novel anti-epileptic drugs. In this study, we explored the multiwell Multi-electrode array (MEA) system as a tool to identify robust network activity parameters in an approach to model mTORopathy-related epilepsy in vitro. To this extent, we cultured mouse primary hippocampal neurons on the multiwell MEA to identify robust network activity phenotypes in mTORC1-hyperactive neuronal networks. mTOR-hyperactivity was induced either through deletion of Tsc1 or overexpression of a constitutively active RHEB variant identified in patients, RHEBp.P37L. mTORC1 dependency of the phenotypes was assessed using rapamycin, and vigabatrin was applied to treat epilepsy-like phenotypes. We show that hyperactivity of the mTORC1 pathway leads to aberrant network activity. In both the Tsc1-KO and RHEB-p.P37L models, we identified changes in network synchronicity, rhythmicity, and burst characteristics. The presence of these phenotypes is prevented upon early treatment with the mTORC1-inhibitor rapamycin. Application of rapamycin in mature neuronal cultures could only partially rescue the network activity phenotypes. Additionally, treatment with the anti-epileptic drug vigabatrin reduced network activity and restored burst characteristics. Taken together, we showed that mTORC1-hyperactive neuronal cultures on the multiwell MEA system present reliable network activity phenotypes that can be used as an assay to explore the potency of new drug treatments targeting epilepsy in mTORopathy patients and may give more insights into the pathophysiological mechanisms underlying epilepsy in these patients.

Stability and synchronization of octonion-valued neural networks with leakage and mixed delays on time scales

There has been a great deal of interest in the last few years for neural networks (NNs) with values in multidimensional domains. The most popular models are complex-valued neural networks (CVNNs), followed by quaternion-valued neural networks (QVNNs), and, more recently, by Clifford-valued neural networks (ClVNNs). However, also very recently, a different type of NNs were put forward, namely octonion-valued neural networks (OVNNs). OVNNs are defined on the 8D octonion algebra, and they are not a special type of ClVNNs, because Clifford numbers are associative, whereas octonions are not. Moreover, beside the complex and quaternion algebras, the only other normed division algebra over the reals is the algebra of octonions, which makes OVNNs a direct generalization of CVNNs and QVNNs from this point of view, raising interest for applications handling high-dimensional data. On the other hand, systems defined on time scales were proposed as a generalization of both discrete time and continuous time systems, or any type of hybrid combination between the two. Finally, time delays appear as a consequence of implementing NNs in real life circuits. Taking all these into consideration, this paper studies the fundamental properties of exponential stability and exponential synchronization for OVNNs with leakage and mixed delays defined on time scales. In order to avoid the problems raised by the non-associativity of the octonion algebra, the OVNN model is decomposed into a real-valued one. Then, two different Lyapunov-type functionals are defined and the particularities of time scale calculus are used in order to deduce sufficient conditions expressed as scalar and linear matrix inequalities (LMIs) for the exponential stability of the proposed models, based on Halanay-type inequalities suitable for time scale systems. Afterwards, a state feedback controller is used to deduce sufficient criteria given as scalar inequalities and LMIs for the exponential synchronization of the same type of models. The generality of the model, given by the definition on the algebra of octonions, the use of different types of delays, and the definition on time scales represent an important advantage. Also, for less general models, it is possible to particularize the obtained results. With the aim to demonstrate each of the paper’s four theorems, four numerical examples are provided.

Adaptive Sliding Mode Fixed-/Preassigned-Time Synchronization of Stochastic Memristive Neural Networks with Mixed-Delays

The paper addresses the fixed-/preassigned-time synchronization of stochastic memristive neural networks (MNNs) with uncertain parameters and mixed delays. Adaptive sliding mode control (ASMC) technology is mainly utilized. First, a proper sliding surface is constructed and the adaptive laws are given. Also, the synchronization control scheme is designed, which can ensure error system to realize fixed-time stability. Second, preassigned-time sliding mode control scheme is mainly provided to realize fast synchronization of MNNs. The presented theoretical methods can guarantee the error system convergence and stability for reaching and sliding mode within preassigned-time. And the synchronization criteria and explicit expression of settling time (ST) are acquired, where ST is not related with initial values and controller parameters but can be predefined perferentially. Finally, the calculation example is offered to interpret the practicability and availability of the innovations in this paper.