Complex Dynamical Networks Research Articles

Epidemic dynamics of complex networks based on information dependence

Epidemic dynamics of complex networks based on information dependence

Finite-time synchronization of complex dynamic networks with impulsive control and actuator saturation: An LMI approach

This paper investigates the finite-time synchronization (FTS) of complex dynamic networks (CDNs) with impulsive control subject to actuator saturation. We develop a novel method that integrates the impulsive comparison principle and improved convex hull representation lemma of saturated function to derive LMI-based sufficient conditions for FTS, which are easy to verify. We also estimate the admissible set of initial values to ensure the validity of the lemma. Unlike previous work, we relax the monotonicity assumption on the Lyapunov function, which broadens our results’ applicability. Moreover, we formulate and solve an optimization problem to enlarge the admissible set under the LMI constraints, using YALMIP toolbox in MATLAB software. Finally, several numerical examples are proposed to demonstrate our results’ effectiveness and superiority.

Robust synchronization of Markovian jump complex dynamical networks under link attacks: Delay-dependent dynamic event-triggered control approach

This paper investigates the synchronization problem for Markovian jump complex dynamical networks (MJCDNs) subject to link attacks. An extended dynamic event-triggered (DET) control is proposed that takes into account limited network resources and time-varying delay constraints. The proposed method enhances the robustness and resource-saving ability of the DET mechanism, and avoids the Zeno phenomenon. It provides MJCDNs to have a buffering ability for external interference. Additionally, this paper introduces a robust model-based strategy to address scenarios where network attackers inject false data into the link channels between nodes. This approach reduces the complexity of processing MJCDNs subject to link attacks. By leveraging network topology and Lyapunov functions, the criteria are derived to achieve robust synchronization of MJCDNs under link attacks. Finally, simulation examples including Chua’s circuit are presented to verify the validity and superiority of the results.

How synchronized human networks escape local minima

Finding the global minimum in complex networks while avoiding local minima is challenging in many types of networks. In human networks and communities, adapting and finding new stable states amid changing conditions due to conflicts, climate changes, or disasters, is crucial. We studied the dynamics of complex networks of violin players and observed that such human networks have different methods to avoid local minima than other non-human networks. Humans can change the coupling strength between them or change their tempo. This leads to different dynamics than other networks and makes human networks more robust and better resilient against perturbations. We observed high-order vortex states, oscillation death, and amplitude death, due to the unique dynamics of the network. This research may have implications in politics, economics, pandemic control, decision-making, and predicting the dynamics of networks with artificial intelligence.

Generalization of neural network models for complex network dynamics

Differential equations are a ubiquitous tool to study dynamics, ranging from physical systems to complex systems, where a large number of agents interact through a graph. Data-driven approximations of differential equations present a promising alternative to traditional methods for uncovering a model of dynamical systems, especially in complex systems that lack explicit first principles. A recently employed machine learning tool for studying dynamics is neural networks, which can be used for solution finding or discovery of differential equations. However, deploying deep learning models in unfamiliar settings-such as predicting dynamics in unobserved state space regions or on novel graphs-can lead to spurious results. Focusing on complex systems whose dynamics are described with a system of first-order differential equations coupled through a graph, we study generalization of neural network predictions in settings where statistical properties of test data and training data are different. We find that neural networks can accurately predict dynamics beyond the immediate training setting within the domain of the training data. To identify when a model is unable to generalize to novel settings, we propose a statistical significance test.

Latency‐Sensitive Service Function Chains Intelligent Migration in Satellite Communication Driven by Deep Reinforcement Learning

ABSTRACTSatellite communication technology solves the problem that the traditional wired network infrastructure is difficult to achieve global communication coverage. However, factors such as satellite orbits introduce frequent changes to the network topology, and challenges like satellite failures and communication link interruptions are prevalent. In the face of these issues, service function chain (SFC) migration becomes a crucial method for swiftly adjusting SFCs during faults, maintaining service continuity and availability. This article proposes a latency‐sensitive SFC migration algorithm tailored to satellite networks. The algorithm first models the satellite network as a multi‐domain virtual network, capturing the constraints faced during SFC migration. Subsequently, a deep reinforcement learning algorithm integrated attention mechanism is designed to more accurately capture and understand the complex network environment and dynamic satellite network topology and derive optimal SFC migration strategies for superior performance. Finally, through experimentation and evaluation of the deep reinforcement learning‐driven latency‐sensitive service function chain intelligent migration algorithm (LS‐SFCM) in satellite communication, this study validates the effectiveness and superior performance of the algorithm in latency‐sensitive scenarios. It provides a new avenue for enhancing the service quality and efficiency of satellite communication networks.

Insight into a new perspective on the complex propagation processes in networks: dynamic link equations

Insight into the spread of epidemics under different transmission mechanisms in networks has long been an important research question in the field of complex network dynamics. Currently, under simple transmission mechanisms, our analysis of the dynamic processes in networks starts only from the node level, considering the scale of infected nodes in the network. However, the information provided by this lowest-order approach to considering dynamic processes in networks is very limited. Most importantly, it is not applicable to the analysis of dynamic processes in networks under more common complex transmission mechanisms, as it neglects the interactions between nodes. Therefore, in this article, we propose a set of closed link dynamic equations to gain insight into complex propagation processes from a microscopic perspective. Fundamentally, we have developed a set of analytical tools for analyzing complex dynamic behaviors at the link level, enabling us to reexamine the complex dynamic processes on networks from a higher-order perspective. Additionally, we apply the proposed analytical framework to complex SIS epidemiological models on two real and synthetic networks, and extensive numerical simulation results demonstrate the feasibility and effectiveness of the proposed method.

Neural relational and dynamics inference for complex systems

Many complex processes in the real world can be viewed as complex systems and their evolution is governed by underlying nonlinear dynamics. However, one can only access the trajectories of the system without knowing the underlying system structure and dynamics in most cases. To address this challenge, this paper proposes a model called Neural Relational and Dynamics Inference (NRDI) that combines graph neural networks (GNNs) and ordinary differential equation systems (ODEs) to handle both continuous-time dynamics prediction and network topology inference for complex systems. Our model contains two modules: (1) the network inference module, which infers system structure from input system trajectories using GNNs, and (2) the dynamics learning module, which employs GNNs to fit the differential equation system for predicting future trajectories. We tested NRDI’s performance on system trajectory prediction and graph reconstruction separately. Experimental results show that the proposed NRDI outperforms many baseline models on continuous-time complex network dynamics prediction, and can explicitly infer network structures with high accuracy.

Fault Tolerant Metric Dimension of Arithmetic Graphs

For a graph G , two vertices x , y ∈ G are said to be resolved by a vertex s ∈ G , if d ( x | s ) ≠ d ( y | s ) . The minimum cardinality of such a resolving set R in G is called its metric dimension. A resolving set R is said to be fault-tolerant, if for every p ∈ R , R − p preserves the property of being a resolving set. A fault-tolerant metric dimension of G is a minimal possible order fault-tolerant resolving set. A wide variety of situations, in which connection, distance, and connectivity are important aspects, call for the utilisation of metric dimension. The structure and dynamics of complex networks, as well as difficulties connected to robotics network design, navigation, optimisation, and facility positioning, are easier to comprehend as a result of this. As a result of the relevant concept of metric dimension, robots are able to optimise their methods of localization and navigation by making use of a limited number of reference locations. As a consequence of this, numerous applications of robotics, including collaborative robotics, autonomous navigation, and environment mapping, have become more precise, efficient, and resilient. The arithmetic graph A l is defined as the graph with its vertex set as the set of all divisors of l , where l is a composite number and l = p γ 1 1 p η 2 2 , … , p n n , where p n ≥ 2 and the p i ’s are distinct primes. Two distinct divisors x , y of l are said to have the same parity if they have the same prime factors (i.e., x = p 1 p 2 and y = p 2 1 p 3 2 have the same parity). Further, two distinct vertices x , y ∈ A l are adjacent if and only if they have different parity and gcd ( x , y ) = p i (greatest common divisor) for some i ∈ { 1 , 2 , … , t } . This article is dedicated to the investigation of the arithmetic graph of a composite number l , which will be referred to throughout the text as A l . In this study, we compute the fault-tolerant resolving set and the fault-tolerant metric dimension of the arithmetic graph A l , where l is a composite number.

Cluster synchronization of complex dynamic networks under pinning control via a limited capacity communication channel

In this paper, the cluster synchronization pinning control problem is investigated for the continuous-time-directed complex dynamic networks under the bit rate constraint. Firstly, a node selection scheme based on differences in node degrees is proposed to achieve cluster synchronization. Subsequently, a coding–decoding scheme is designed during data transmission through digital communication channels where only a limited number of encoded signal sequences are sent to the controller side. Further, regarding the unreliability of the channel, the phenomenon of packet dropouts is considered during the encoding process, which is modeled by using a series of independent Bernoulli distributed random variables. The pinning controller is then designed based on the received decoding information. By means of the convex optimization method, a sufficient condition is established to ensure that the cluster synchronization error is ultimately bounded and the desired controller gain is determined based on the solution to matrix inequalities. Finally, the effectiveness of the obtained results is validated through a simulation example.

Synchronization on complex dynamical networks via intermittently sampled-data pinning control

Each specific control strategy has a unique advantage, and combining multiple control strategies can harness the advantages of these strategies. Designing new control strategies by integrating different control strategies is an interesting and challenging topic. This paper introduces an intermittently sampled-data pinning (ISP) control strategy, which merges intermittent control, sampled-data control and pinning control, to study synchronization on complex dynamical networks. The ISP control strategy is proposed to solve three difficulties: first, the controllers transmitting feedback signals may be discontinuous; second, the controllers often cannot operate continuously in practical applications; third, it is usually hard to control all nodes in a dynamical network as the network size is huge. Sufficient conditions are obtained for realizing synchronization on dynamical networks. Furthermore, time delays are incorporated into the proposed control strategy to address the untimely reception of feedback signals and achieve the synchronization conditions on dynamical networks. Finally, two numerical examples demonstrate the effectiveness of the proposed control method.

Output synchronization of a class of complex dynamic networks: A reinforcement learning method

In this paper, to achieve the synchronization control for a class of complex dynamic networks with completely unknown system dynamics, a reinforcement learning output feedback algorithm based on state reconstruction is proposed. Given the high cost and complexity associated with obtaining the full state information, an output-based node state reconstruction method is employed for the first time in complex dynamic networks. The proposed method utilizes a sequence composed of a finite number of output data to reconstruct the current state. At the same time, the overall error system is constructed to handle the coupling relationship between nodes, to facilitate the controller design. Thereafter, considering the system dynamics are unknown, an algorithm based on reinforcement learning is proposed to ensure rapid synchronization of node outputs, and the convergence of proposed method is proven. Finally, the feasibility of proposed algorithm is corroborated through a simulation example and a multi-vehicle system.

Input–Output Finite-Time Bipartite Synchronization for Multiweighted Complex Dynamical Networks Under Dynamic Hybrid Triggering Mechanism

Abstract The problem of input–output finite-time (IO-FT) bipartite synchronization for a class of nonlinear multiweighted complex dynamical networks (CDNs) in the presence of multiple coupling delays, external disturbances, and deception attacks is explored in this study. To be precise, the limited communication resources have been mitigated with the aid of undertaken hybrid triggered strategy, which reduces the unwanted network transmission and simultaneously improves the system's performance. Specifically, in the hybrid-trigger scheme, a Bernoulli distributed random variable has been employed to switch between the two communication channels. Moreover, the event-triggered scheme involving the dynamic trigger conditions is incorporated in the sensor-to-controller, which reduces the number of triggers compared to static event-triggered strategy. Further, the adequate conditions are derived in terms of linear matrix inequalities by constructing a Lyapunov–Krasovskii functional candidate. In light of this, the required parameters involved in triggering and the gain matrix are acquired by solving the developed linear matrix inequalities. Eventually, the reliability of the developed approach is verified via the illustration of two numerical examples, including the Chua's circuit with simulation verifications.

Complex Dynamic Networks for Multiple Attacks: A Jump-Like Event-Triggered Controller Based on Neural Network Model

Complex Dynamic Networks for Multiple Attacks: A Jump-Like Event-Triggered Controller Based on Neural Network Model

Asymptotical Tracking Control of Complex Dynamical Network Based on Links State Observer

Asymptotical Tracking Control of Complex Dynamical Network Based on Links State Observer

Analyst network centrality, forecast accuracy, and persistent influence

ABSTRACT This paper explores how analysts’ forecasting behaviour is related to their centrality within a dynamic information network. In this network, analysts who issued coverage reports on the same listed firms in clusters are connected. The social learning hypothesis and social capital theory suggest that financial analysts could learn from other analyst forecasts and obtain information from analyst reports. Employing a dynamic complex network methodology, we focus on analysts’ network centrality – degree, betweenness, and closeness – to represent their information access based on a sample of 819,539 analyst forecasts in the Chinese A-share market from 2018 to 2022. Our findings suggest that analysts with more central positions in the network produce more accurate earnings-per-share forecasts and have a longer persistent influence on other analysts. Our results support the perspective that the diffusion of information among analysts affects their forecasts and reporting behaviour.

Wealth distribution on a dynamic complex network

We present an agent-based model that examines the microscopic exchange of wealth in a dynamic network to investigate the topological characteristics associated with economic inequality. The model consists of two processes: conservative wealth exchange between connected agents and the rewiring of connections, which depends on the wealth of the agents. The dynamics of wealth and connections are interrelated, as the network structure influences which agents interact with each other. We analyze the time evolution and asymptotic characteristics of the model for different values of a social protection factor (f), which favors the poorest agent in each wealth transaction. Our results show that for f=0, wealth and connections condense in a single agent, in accordance with mean-field models of wealth exchange. When f is low, agents from the middle and upper classes become favored, leading to the formation of network hubs. However, as f increases, the restriction of the network on exchanges results in an egalitarian society departing from the outcomes observed in the mean-field exchange models.

Dynamic behavior and driving region of spray combustion instability in a backward-facing step combustor.

We numerically study the dynamic behavior and driving region of spray combustion instability in a backward-facing step combustor using analytical methodologies based on dynamical systems theory, symbolic dynamics, complex networks, and machine learning. The global dynamic behavior of a heat release rate field represents low-dimensional chaotic oscillations with deterministically aperiodic intercycle dynamics. Spray combustion instability is driven in the formation and separation region of a large-scale organized vortex induced by the hydrodynamic shear layer instability at the edge of the backstep. This region corresponds fairly to that of the hub in an acoustic-energy-flux-based spatial network. The feature importance in a random forest is valid for clarifying the feedback coupling of spray combustion instability.

Reputation-based disconnection-reconnection mechanism in Prisoner's Dilemma Game within dynamic networks

Individual reputation significantly influences players’ decision-making. Players tend to disconnect from neighbors with lower reputations so as to mitigate potential losses in the game. Therefore, it is crucial and meaningful to explore how to apply reputation in the game to enhance cooperation. In this study, we propose a reputation-based evolution mechanism in the Prisoner's Dilemma Game (PDG) within dynamic complex networks, including square lattices and small-world networks. We introduce the reputation factor α and the selection intensity σ in order to measure the changes in reputation and their impact objectively. Moreover, considering the impact of information connectivity, we define the environmental degree r and investigate the effects of environmental degree r and rewiring probability p on cooperation rates. Simulation results demonstrate that the reputation factor and information connectivity have a positive promoting effect on cooperative behavior; conversely, the increase in selection intensity affects cooperation negatively.

Fixed-time synchronization of multilayered complex dynamic networks via quantized variable-gain saturated control

This paper studies fixed-time (FxT) quantitative synchronization of multilayered complex dynamic networks (CDNs). First, a new FxT stability theorem is established and two new estimations of the settling time of stability are acquired, which are more accurate than the existing ones. Then, by using the improved theorem, several sufficient conditions ensuring FxT synchronization of a multilayered CDN are derived via two classes of innovative quantized variable-gain saturated controllers, and some high-precision estimates of the synchronous settling time (SST) are attained. In general, the saturation function used to replace the signum function is nonlinear and even includes the odd-even requirement on the exponent, and no quantization is involved in the developed FxT controllers. However, in our design, the classical linear saturation function is employed and the input signals of the controllers are also quantized. Therefore, our proposed strategies are more practical and easier to implement. Besides, different from the traditional 2-norm/1-norm-based approaches, a novel nonsmooth Lyapunov function is constructed so that the resultant estimates of the SST are unrelated to either the network size or the node's dimension, which are less conservative and closer to the actual synchronized time. Lastly, some numerical examples are given to validate the theoretical results.