Complex Spatio-temporal Networks Research Articles

Boundary control for synchronization of fractional-order complex spatiotemporal networks based on PDEs with multiple delays and its application in image encryption

This paper addresses the synchronization problem of fractional-order complex spatiotemporal networks (CSNs) based on partial differential equations with delays via boundary control. First, fractional-order CSNs with time-invariant and time-varying delays are studied separately due to the widespread existence of time delays in complex networks. Moreover, two boundary controllers are proposed to solve the synchronization issue of fractional-order CSNs, in which nodes communicate with each other only on the spatial boundary. Furthermore, according to the fractional-order inequality, the synchronization criteria of fractional-order CNSs with multiple delays are obtained. Finally, the numerical simulations are given to verify the feasibility of the presented results. A case provides the application of CSNs in image encryption.

Adaptive control for synchronization of semi‐linear complex spatio‐temporal networks with time‐invariant coupling delay and time‐variant coupling delay

SummaryThis article studies the adaptive control for synchronization of semi‐linear complex spatio‐temporal networks (CSNs). And the leader‐following and leaderless CSN with time‐invariant coupling delay and time‐variant coupling delay are developed separately from two aspects. The adaptive control strategies are proposed to reach the asymptotic convergence of synchronization error. Synchronization criteria and sufficient conditions are obtained for the leader‐following CSN error model and leaderless CSN error model by constructing the apposite Lyapunov–Krasovskii functions and applying Wirtinger's inequality. Finally, two experimental examples are given to verify the feasibility of the theories proposed in this article.

Exponential Synchronization of Hyperbolic Complex Spatio-Temporal Networks with Multi-Weights

This paper deals with the leader-following synchronization of first-order, semi-linear, complex spatio-temporal networks. Firstly, two sorts of complex spatio-temporal networks based on hyperbolic partial differential equations (CSTNHPDEs) are built: one with a single weight and the other with multi-weights. Then, a new distributed controller is designed to address CSTNHPDE with a single weight. Sufficient conditions for the synchronization and exponential synchronization of CSTNHPDE are presented by showing the gain ranges. Thirdly, the proposed distributed controller addresses of CSTNHPDE with multi-weights, and gain ranges are obtained for synchronization and exponential synchronization, respectively. Finally, two examples show the effectiveness and good performance of the control methods.

Synchronization of Nonlinear Complex Spatiotemporal Networks Based on PIDEs with Multiple Time Delays: A P-sD Method

This paper studies the synchronization control of nonlinear multiple time-delayed complex spatiotemporal networks (MTDCSNs) based on partial integro-differential equations. Firstly, dealing with an MTDCSN with time-invariant delays, P-sD control is employed and the synchronization criteria are obtained in terms of LMIs. Secondly, this control method is further used in an MTDCSN with time-varying delays. An example illustrates the effectiveness of the proposed methods.

Finite Time Synchronization for Reactive Diffusion Complex Networks via Boundary Control

This paper investigates the finite-time synchronization problems of complex spatiotemporal networks with time delays and diffusion terms. First, a boundary controller based on Lyapunov stability theory, Wirtinger's inequality, and finite-time analysis is designed. Subsequently, sufficient conditions for finite-time synchronization are obtained, and the setting time of finite-time synchronization is estimated. Finally, a simulation example is given to demonstrate the effectiveness of the obtained result.

Synchronization for Nonlinear Complex Spatio-Temporal Networks with Multiple Time-Invariant Delays and Multiple Time-Varying Delays

This paper deals with the problem for synchronization of a nonlinear time delayed complex spatio-temporal network (CSN), modelled by semi-linear parabolic partial differential-difference equations. A boundary controller relying to distributed measurement is designed. Multiple time-invariant delays are firstly considered. By employing Lyapunov’s direct method and Wirtingers inequality, synchronization criteria of the CSN are presented in terms of LMIs. And then, multiple time-varying delays are respectively considered using the boundary controller and synchronization criteria are obtained. Finally, an example illustrates the effectiveness of the proposed method.

Event-Related Potential Responses to Task Switching Are Sensitive to Choice of Spatial Filter.

Event-related potential (ERP) studies using the task-switching paradigm show that multiple ERP components are modulated by activation of proactive control processes involved in preparing to repeat or switch task and reactive control processes involved in implementation of the current or new task. Our understanding of the functional significance of these ERP components has been hampered by variability in their robustness, as well as their temporal and scalp distribution across studies. The aim of this study is to examine the effect of choice of reference electrode or spatial filter on the number, timing and scalp distribution of ERP elicited during task-switching. We compared four configurations, including the two most common (i.e., average mastoid reference and common average reference) and two novel ones that aim to reduce volume conduction (i.e., reference electrode standardization technique (REST) and surface Laplacian) on mixing cost and switch cost effects in cue-locked and target-locked ERP waveforms in 201 healthy participants. All four spatial filters showed the same well-characterized ERP components that are typically seen in task-switching paradigms: the cue-locked switch positivity and target-locked N2/P3 effect. However, both the number of ERP effects associated with mixing and switch cost, and their temporal and spatial resolution were greater with the surface Laplacian transformation which revealed rapid temporal adjustments that were not identifiable with other spatial filters. We conclude that the surface Laplacian transformation may be more suited to characterize EEG signatures of complex spatiotemporal networks involved in cognitive control.

Synchronization of Nonlinear Complex Spatio-Temporal Networks Using Adaptive Boundary Control and Pinning Adaptive Boundary Control

There are many behaviors with spatio-temporal characteristics in nature. Complex spatio-temporal networks (CSNs)-based on partial differential equations are to process such issues. This paper studies two synchronization boundary control methods. An adaptive boundary controller is first studied to ensure synchronization of the CSNs. Furthermore, a pinning adaptive boundary controller is proposed to achieve synchronization of the CSNs. Two sufficient criteria of synchronization and pinning synchronization are respectively obtained. Finally, two numerical examples demonstrate the effectiveness of the proposed theoretical results.

Finite-time topology identification of complex spatio-temporal networks with time delay

This paper presents two methods for finite-time topology identification for the complex spatio- temporal networks with coupling time delay. By introducing the auxiliary systems, a relationship between the unknown topology and two measurable matrix signals is developed. Based on the relationship, one method of identifying the topology is to compute the invertibility of the matrix. Besides this method, an adaptive law is developed to infer the topology online in finite time. The proposed methods do not require the differentiability of the time-varying delay. Furthermore, the methods can also be applied to complex spatio-temporal networks with unknown system parameters. Finally, an illustrative example is provided to show the effectiveness of the proposed methods.

Topology identification of a class of complex spatio‐temporal networks with time delay

The problem of topology identification is valuable to understand and control complex networks. Furthermore, many complex networks are spatio-temporal in the real world. This study proposes a method to identify the topology of complex spatio-temporal networks with coupling time delay. Adaptive observer and novel updating laws are designed to provide the estimation of the topology. Finally, a numerical example is given to demonstrate the effectiveness of the proposed method. The result is general and can be applicable to contemporary network science and engineering.

Projective Exponential Synchronization for a Class of Complex PDDE Networks with Multiple Time Delays

This paper addresses the problem of projective exponential synchronization for a class of complex spatiotemporal networks with multiple time delays satisfying the homogeneous Neumann boundary conditions, where the network is modeled by coupled partial differential-difference equations (PDDEs). A distributed proportional-spatial derivative (P-sD) controller is designed by employing Lyapunov’s direct method and Kronecker product. The controller ensures the projective exponential synchronization of the PDDE network. The main result of this paper is presented in terms of standard linear matrix inequality (LMI). A numerical example is provided to show the effectiveness of the proposed design method.

Exponential synchronization for a class of complex spatio-temporal networks with space-varying coefficients

This paper addresses the problem of exponential synchronization for a class of complex spatio-temporal networks with space-varying coefficients, where the dynamics of nodes are described by coupled partial differential equations (PDEs). The goal of this research is to design distributed proportional-spatial derivative (P-sD) state feedback controllers to ensure exponential synchronization of the complex spatio-temporal network. Using Lyapunov׳s direct method, the problem of exponential synchronization of the complex spatio-temporal network is formulated as the feasibility problem of spatial differential linear matrix inequality (SDLMI) in space. The feasible solutions to this SDLMI in space can be approximately derived via the standard finite difference method and the linear matrix inequality (LMI) optimization technique. Finally, a numerical example is presented to demonstrate the effectiveness of the proposed design method.