Networks Of Dynamical Systems Research Articles

Dynamical Analysis and Synchronization of Complex Network Dynamic Systems under Continuous-Time

In multilayer complex networks, the uncertainty in node states leads to intricate behaviors. It is, therefore, of great importance to be able to estimate the states of target nodes in these systems, both for theoretical advancements and practical applications. This paper introduces a state observer-based approach for the state estimation of such networks, focusing specifically on a class of complex dynamic networks with nodes that correspond one-to-one. Initially, a chaotic system is employed to model the dynamics of each node and highlight the essential state components for analysis and derivation. A network state observer is then constructed using a unique diagonal matrix, which underpins the driver and response-layer networks. By integrating control theory and stability function analysis, the effectiveness of the observer in achieving synchronization between complex dynamic networks and target systems is confirmed. Additionally, the efficacy and precision of the proposed method are validated through simulation.

Distributed Reinforcement Learning for Networked Dynamical Systems

Distributed Reinforcement Learning for Networked Dynamical Systems

Sustainability under Active Inference

In this paper, we explore the known connection among sustainability, resilience, and well-being within the framework of active inference. Initially, we revisit how the notions of well-being and resilience intersect within active inference before defining sustainability. We adopt a holistic concept of sustainability denoting the enduring capacity to meet needs over time without depleting crucial resources. It extends beyond material wealth to encompass community networks, labor, and knowledge. Using the free energy principle, we can emphasize the role of fostering resource renewal, harmonious system–entity exchanges, and practices that encourage self-organization and resilience as pathways to achieving sustainability both as an agent and as a part of a collective. We start by connecting active inference with well-being, building on existing work. We then attempt to link resilience with sustainability, asserting that resilience alone is insufficient for sustainable outcomes. While crucial for absorbing shocks and stresses, resilience must be intrinsically linked with sustainability to ensure that adaptive capacities do not merely perpetuate existing vulnerabilities. Rather, it should facilitate transformative processes that address the root causes of unsustainability. Sustainability, therefore, must manifest across extended timescales and all system strata, from individual components to the broader system, to uphold ecological integrity, economic stability, and social well-being. We explain how sustainability manifests at the level of an agent and then at the level of collectives and systems. To model and quantify the interdependencies between resources and their impact on overall system sustainability, we introduce the application of network theory and dynamical systems theory. We emphasize the optimization of precision or learning rates through the active inference framework, advocating for an approach that fosters the elastic and plastic resilience necessary for long-term sustainability and abundance.

Intellectual Property Law's Confiscatory Losses: Its Application in Dynamic Network Environments

This paper discusses confiscatory losses in the dynamic network enforcement of intellectual property (IP). IP law protects copyrights, patents, and trademarks. Instead, IP enforcement may consequence in "confiscatory damages." This occurs when the defendant's property is apprehended pursuant to a court order. For both individuals and companies, the internet has made sharing and disseminating innovative creations simpler. IP infringement is also increased by this. In these circumstances, IP law enforcement has become more crucial. Penalisations and sanctions for IP infringement in these conditions may be severe and upshot in confiscatory losses. So as to apply confiscatory losses in dynamic network conditions, this paper suggests reviewing IP law enforcement strategies. Hence, IP infringement penalisations and compensation should be proportionate to the harm caused and avoid confiscatory losses. Moreover, IP infringement can also be minimized by education, information, and alternative dispute resolution. IP law enforcement in dynamic network systems must strike a compromise between protecting IP rights and sidestepping confiscatory damages.

Learning the Causal Structure of Networked Dynamical Systems under Latent Nodes and Structured Noise

This paper considers learning the hidden causal network of a linear networked dynamical system (NDS) from the time series data at some of its nodes -- partial observability. The dynamics of the NDS are driven by colored noise that generates spurious associations across pairs of nodes, rendering the problem much harder. To address the challenge of noise correlation and partial observability, we assign to each pair of nodes a feature vector computed from the time series data of observed nodes. The feature embedding is engineered to yield structural consistency: there exists an affine hyperplane that consistently partitions the set of features, separating the feature vectors corresponding to connected pairs of nodes from those corresponding to disconnected pairs. The causal inference problem is thus addressed via clustering the designed features. We demonstrate with simple baseline supervised methods the competitive performance of the proposed causal inference mechanism under broad connectivity regimes and noise correlation levels, including a real world network. Further, we devise novel technical guarantees of structural consistency for linear NDS under the considered regime.

Higher-order Granger reservoir computing: simultaneously achieving scalable complex structures inference and accurate dynamics prediction

Recently, machine learning methods, including reservoir computing (RC), have been tremendously successful in predicting complex dynamics in many fields. However, a present challenge lies in pushing for the limit of prediction accuracy while maintaining the low complexity of the model. Here, we design a data-driven, model-free framework named higher-order Granger reservoir computing (HoGRC), which owns two major missions: The first is to infer the higher-order structures incorporating the idea of Granger causality with the RC, and, simultaneously, the second is to realize multi-step prediction by feeding the time series and the inferred higher-order information into HoGRC. We demonstrate the efficacy and robustness of the HoGRC using several representative systems, including the classical chaotic systems, the network dynamical systems, and the UK power grid system. In the era of machine learning and complex systems, we anticipate a broad application of the HoGRC framework in structure inference and dynamics prediction.

Efficient parameter inference in networked dynamical systems via steady states: A surrogate objective function approach integrating mean-field and nonlinear least squares.

In networked dynamical systems, inferring governing parameters is crucial for predicting nodal dynamics, such as gene expression levels, species abundance, or population density. While many parameter estimation techniques rely on time-series data, particularly systems that converge over extreme time ranges, only noisy steady-state data is available, requiring a new approach to infer dynamical parameters from noisy observations of steady states. However, the traditional optimization process is computationally demanding, requiring repeated simulation of coupled ordinary differential equations. To overcome these limitations, we introduce a surrogate objective function that leverages decoupled equationsto compute steady states, significantly reducing computational complexity. Furthermore, by optimizing the surrogate objective function, we obtain steady states that more accurately approximate the ground truth than noisy observations and predict future equilibria when topology changes. We empirically demonstrate the effectiveness of the proposed method across ecological, gene regulatory, and epidemic networks. Our approach provides an efficient and effective way to estimate parameters from steady-state data and has the potential to improve predictions in networked dynamical systems.

Heteroclinic dynamics in network dynamical systems with higher-order interactions

Abstract Heteroclinic structures organize global features of dynamical systems. We analyse whether heteroclinic structures can arise in network dynamics with higher-order interactions which describe the nonlinear interactions between three or more units. We find that while commonly analysed model equations such as network dynamics on undirected hypergraphs may be useful to describe local dynamics such as cluster synchronization, they give rise to obstructions that allow to design of heteroclinic structures in phase space. By contrast, directed hypergraphs break the homogeneity and lead to vector fields that support heteroclinic structures.

Automatic Proper Orthogonal Block Decomposition method for network dynamical systems with multiple timescales

In this work, we introduce a novel reduced order model technique, based on the Proper Orthogonal Decomposition method, for dynamical systems with multiple timescales. The main ideas are to retain the structure of the original model, which is lost in the original POD procedure, while producing a competitive reduction in the number of equations and computational time, and to determine the best structure for the reduced system automatically, via a data-driven analysis of the original model data. For these novel techniques, we present some numerical tests for various behaviors of three different neural network models with multiple timescales, which support the use of these new methods.

Practical Cyber Attack Detection With Continuous Temporal Graph in Dynamic Network System

Practical Cyber Attack Detection With Continuous Temporal Graph in Dynamic Network System

Improved zeroing neural models based on two novel activation functions with exponential behavior

A family of zeroing neural networks based on new nonlinear activation functions is proposed for solving various time-varying linear matrix equations (TVLME). The proposed neural network dynamical systems, symbolized as Li-VPZNN1 and Li-VPZNN2, include an exponential parameter in nonlinear activation function (AF) that leads to faster convergence to the theoretical result compared to previous categories of nonlinearly activated neural networks. Theoretical analysis as well as numerical tests in MATLAB's environment confirm the efficiency and accelerated convergence property of the novel dynamics.

TEMPO bacterial cellulose and MXene nanosheets synergistically promote tough hydrogels for intelligent wearable human-machine interaction

Conductive hydrogels have received increasing attention in the field of wearable electronics, but they also face many challenges such as temperature tolerance, biocompatibility, and stability of mechanical properties. In this paper, a double network hydrogel of MXene/TEMPO bacterial cellulose (TOBC) system is proposed. Through solvent replacement, the hydrogel exhibits wide temperature tolerance (−20–60 °C) and stable mechanical properties. A large number of hydrogen bonds, MXene/TOBC dynamic three-dimensional network system, and micellar interactions endow the hydrogel with excellent mechanical properties (elongation at break ~2800 %, strength at break ~420 kPa) and self-healing ability. The introduction of tannic acid prevents the oxidation of MXene and the loss of electrical properties of the hydrogel. In addition, the sensor can also quickly (74 ms) and sensitive (gauge factor = 15.65) wirelessly monitor human motion, and the biocompatibility can well avoid the stimulation when it comes into contact with the human body. This series of research work reveals the fabrication of MXene-like flexible wearable electronic devices based on self-healing, good cell compatibility, high sensitivity, wide temperature tolerance and durability, which can be used in smart wearable, wireless monitoring, human-machine Interaction and other aspects show great application potential.

A hybrid framework of dynamic periodic event-triggered networked control systems subject to time-varying delays

This paper investigates the dynamic output-feedback control for networked control systems (NCSs). The data transmissions in the sensor-to-controller and the controller-to-actuator channels are generated by the dynamic periodic event-triggering mechanism. Due to the existence of time-varying delays in the two channels, the updated data is received after a time delay. To cope with this problem, a hybrid dynamical framework of the NCSs is established. With the help of Lyapunov function-based approach, a new event-triggering condition is designed and sufficient conditions on input-to-state stability are derived. By introducing an auxiliary function, the obtained sufficient conditions are transformed into linear matrix inequalities and the explicit forms of the dynamic output-feedback controller gains are provided. Moreover, the upper bounds on the maximum allowable transfer intervals and the maximum allowable delays are derived. Finally, a numerical example illustrates the feasibility of the proposed method.

On a framework of data assimilation for hyperparameter estimation of spiking neuronal networks

When handling real-world data modeled by a complex network dynamical system, the number of the parameters is often much more than the size of the data. Therefore, in many cases, it is impossible to estimate these parameters and the exact value of each parameter is frequently less interesting than the distribution of the parameters. In this paper, we aim to estimate the distribution of the parameters in the mesoscopic neuronal network model from the macroscopic experimental data, for example, the BOLD (blood oxygen level dependent) signal. Herein, we assume that the parameters of the neurons and synapses are inhomogeneous but independently and identically distributed from certain distributions with unknown hyperparameters. Thus, we estimate these hyperparameters of the distributions of the parameters, instead of estimating the parameters themselves. We formulate this problem under the framework of data assimilation and hierarchical Bayesian method and present an efficient method named Hierarchical Data Assimilation (HDA) to conduct the statistical inference on the neuronal network model with the BOLD signal data simulated by the hemodynamic model. We consider the Leaky Integral-Fire (LIF) neuronal networks with four synapses and show that the proposed algorithm can estimate the BOLD signals and the hyperparameters with high preciseness. In addition, we discuss the influence on the performance of the algorithm configuration and the LIF network model setup.

Development of Pharmacovigilance System in India and Paradigm of Pharmacovigilance Research: An Overview.

The drugs are projected to cure, prevent and treat diseases; however, there are also chances of mild or severe adverse drug reactions (ADRs) in the patients. Pharmacovigilance (PV) enhances the approach to safe medicines and healthcare, but integration into public healthcare remains a challenge in many countries. The Pharmacovigilance Programme of India (PvPI) is a nationwide programme launched by the Ministry of Health and Family Welfare (MoHFW), Government of India, on 14 July 2010. It is currently run by the Indian Pharmacopoeia Commission (IPC). Presently, 567 ADR Monitoring Centres (AMC) are functioning under PvPI across India. The Central Drugs Standard Control Organization (CDSCO), under the Directorate General of Health Services (DGHS), and the Ministry of Health, Family & Welfare (MoHFW) Government of India is the National Regulatory Authority (NRA) of India. This review aims to trace the development of PV in India and its status among the top ADR reporting countries, with a focus on the current status of the studied ADR in different regions in India. Among the top 20 countries enthusiastic about sending ICSR per million population between 2015 and 2020, India shares 2% of the total ICSRs in VigiBase. India is now being recognized as a hub of global clinical trials and clinical research studies. Hence, it is the need of the hour in India to have a dynamic PV network system with an efficient and prudent operation method. Nevertheless, in India, PV programs are at an early stage on par with other countries, and only because of underreporting of ADRs. However, in the future, PvPI may appear as a big dashboard for ADR reporting culture in India as it continuously works hard to improve patients and drug safety.

Event-triggered H∞ control for networked dynamic system with nonideal interconnection

This paper studies the event-triggered H∞ control problem of the networked dynamic system composed of heterogeneous subsystems with nonideal interconnection. Firstly, the considered system is transformed into a time-delay system of high dimension on the basis of well-posedness. Then, a lemma is derived by constructing a sampled-data-dependent Lyapunov functional to ensure the stability with a given H∞ performance of the time-delay system. Next, by fully using the information of the interconnected structure, sufficient conditions that only involve individual subsystem's parameters are established to guarantee the well-posedness, stability and H∞ performance of the controlled networked dynamic system. Based on these conditions, the simultaneous design for the controller gain and the trigger weight matrix is achieved. Finally, the effectiveness of the obtained co-design method is certified by two examples.

The recoverability of network controllability with respect to node additions

Network controllability is a critical attribute of dynamic networked systems. Investigating methods to restore network controllability after network degradation is crucial for enhancing system resilience. In this study, we develop an analytical method based on degree distributions to estimate the minimum fraction of required driver nodes for network controllability under random node additions after the random removal of a subset of nodes. The outcomes of our method closely align with numerical simulation results for both synthetic and real-world networks. Additionally, we compare the efficacy of various node recovery strategies across directed Erdös–Rényi (ER) networks, swarm signaling networks (SSNs), and directed Barabàsi Albert (BA) networks. Our findings indicate that the most efficient recovery strategy for directed ER networks and SSNs is the greedy strategy, which considers node betweenness centrality. Similarly, for directed BA networks, the greedy strategy focusing on node degree centrality emerges as the most efficient. These strategies outperform recovery approaches based on degree centrality or betweenness centrality, as well as the strategy involving random node additions.

Localized and Incremental Probabilistic Inference for Large-Scale Networked Dynamical Systems

Localized and Incremental Probabilistic Inference for Large-Scale Networked Dynamical Systems

Dynamic Neural Network for Bicriteria Weighted Control of Robot Manipulators.

In recent years, bicriteria optimization schemes for manipulator control have become preferred by researchers, given their satisfactory performance. In this article, a bicriteria weighted (BCW) scheme to remedy joint drift and minimize the infinity norm of joint velocity is proposed. The scheme adopts a novel repetitive motion index that can theoretically decouple the joint error and the position error, which many conventional cyclic motion generation schemes cannot achieve. Subsequently, through transformation, the BCW scheme is converted into a time-varying quadratic programming (QP) problem. Then, a dynamic neural network (DNN) system with a new Fisher-Burmeister function is proposed to address the resulting QP problem. It is proven that the proposed DNN system is free of residual errors, which means that the actual solution is able to converge to the theoretical solution. Another essential feature of the DNN system is that it has a suppression effect on noise. To demonstrate the convergence and robustness of the proposed DNN system, comparative simulations are carried out in nominal and noisy environments. Finally, experiments on Franka Emika Panda are conducted to elucidate the availability of the BCW scheme addressed by the DNN system.

Network dynamics with higher-order interactions: coupled cell hypernetworks for identical cells and synchrony

Network interactions that are nonlinear in the state of more than two nodes—also known as higher-order interactions—can have a profound impact on the collective network dynamics. Here we develop a coupled cell hypernetwork formalism to elucidate the existence and stability of (cluster) synchronization patterns in network dynamical systems with higher-order interactions. More specifically, we define robust synchrony subspace for coupled cell hypernetworks whose coupling structure is determined by an underlying hypergraph and describe those spaces for general such hypernetworks. Since a hypergraph can be equivalently represented as a bipartite graph between its nodes and hyperedges, we relate the synchrony subspaces of a hypernetwork to balanced colourings of the corresponding incidence digraph.