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Pinning Control and Controllability of Complex Dynamical Networks

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International Journal of Automation and computing 2017年第1期14卷 1-9页

作者： guanrong chen Department of Electronic Engineering City University of Hong Kong Hong Kong China

In this article, the notion of pinning control for directed networks of dynamical systems is introduced, where the nodes could be either single-input single-output （SISO） or multi-input multi-output （MIMO） dynamical systems, and could be non-identical and nonlinear in general but will be specified to be identical linear time-invariant （LTI） systems here in the study of network controllability. Both state and structural controllability problems will be discussed, illustrating how the network topology, node-system dynamics, external control inputs and inner dynamical interactions altogether affect the controllability of a general complex network of LTI systems, with necessary and sufficient conditions presented for both SISO and MIMO settings. To that end, the controllability of a special temporally switching directed network of linear time-varying （LTV） node systems will be addressed, leaving some more general networks and challenging issues to the end for research outlook.

关键词： Complex network pinning control controllability linear time-invarJant (LTI) system temporally switching network,graph theory.

Generating Lorenz-like and chen-like attractors from a simple algebraic structure

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Science China(Information Sciences) 2014年第7期57卷 214-220页

作者： WANG Xiong chen guanrong Department of Electronic Engineering City University of Hong Kong

This paper reports the finding of a very simple one-parameter family of three-dimensional quadratic autonomous chaotic *** algebraic structure is simple with only four linear terms and two quadratic *** quadratic terms are different from the Lorenz and the chen ***,by tuning the only parameter,this new family of systems can also generate both Lorenz-like and chen-like attractors,thus further reveal the close relation between them.

关键词： chaotic attractor Lorenz system chen system

Discrete chaos in Banach spaces

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Science China Mathematics 2005年第2期48卷 222-238页

作者： SHI Yuming chen guanrong Department of Mathematics Shandong UniversityJina 250100China Department of Electronic EngineeringCity University of Hong KongChina

This paper is concerned with chaos in discrete dynamical systems governed by continuously Frech@t differentiable maps in Banach spaces. A criterion of chaos induced by a regular nondegenerate homoclinic orbit is established. Chaos of discrete dynamical systems in the n-dimensional real space is also discussed, with two criteria derived for chaos induced by nondegenerate snap-back repellers, one of which is a modified version of Marotto's theorem. In particular, a necessary and sufficient condition is obtained for an expanding fixed point of a differentiate map in a general Banach space and in an n-dimensional real space, respectively. It completely solves a long-standing puzzle about the relationship between the expansion of a continuously differentiable map near a fixed point in an n-dimensional real space and the eigenvalues of the Jacobi matrix of the map at the fixed point.

关键词： chaos, discrete dynamical system, Banach space, Marotto's theorem.

Simplicial networks:a powerful tool for characterizing higher-order interactions

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National Science Review 2022年第5期9卷 79-80页

作者： Dinghua Shi guanrong chen Department of Mathematics College of ScienceShanghai University Department of Electronic Engineering City University of Hong Kong

In recent network research,more and more efforts have been devoted to studying higher-order interactions in complex networks that explain some intrinsic properties,discover hidden features that conventional mathematical tools cannot help to find and enable a clearer view of the re al *** article presents a perspective on the state-of-the-art progress in the field.

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Computing Persistent Homology by Spanning Trees and Critical Simplices

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Research 2024年第2期2023卷 519-527页

作者： Dinghua Shi Zhifeng chen Chuang Ma guanrong chen Department of Mathematics Cllege of ScienceShanghai UniversityShanghaiChina School of Big Data Fuzhou University of International Studies and TradeFuzhouChina Department of Data Science and Big Data Technology School of InternetAnhui UniversityHefeiChina Department of Electrical Engineering City University of Hong KongHong KongChina

Topological data analysis can extract effective information from higher-dimensional *** mathematical basis is persistent *** persistent homology can calculate topological features at different spatiotemporal scales of the dataset,that is,establishing the integrated taxonomic relation among points,lines,and ***,the simplicial network composed of all-order simplices in a simplicial complex is *** the sequence of nested simplicial subnetworks can be regarded as a discrete Morse function from the simplicial network to real values,a method based on the concept of critical simplices can be developed by searching all-order spanning *** this new method,not only the Morse function values with the theoretical minimum number of critical simplices can be obtained,but also the Betti numbers and composition of all-order cavities in the simplicial network can be calculated ***,this method is used to analyze some examples and compared with other methods,showing its effectiveness and feasibility.

关键词： Morse establishing topological

Totally homogeneous networks

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National Science Review 2019年第5期6卷 962-969页

作者： Dinghua Shi Linyuan Lü guanrong chen Department of Mathematics College of Science Shanghai University Institute of Fundamental and Frontier Sciences University of Electronic Science and Technology of China Department of Electronic Engineering City University of Hong Kong

In network science, the non-homogeneity of node degrees has been a concerning issue for ***, with today’s modern web technologies, the traditional social communication topologies have evolved from node-central structures into online cycle-based communities, urgently requiring new network theories and *** the focus from node degrees to network cycles could reveal many interesting properties from the perspective of totally homogenous networks or sub-networks in a complex network, especially basic simplexes(cliques) such as links and ***, compared with node degrees, it is much more challenging to deal with network *** studying the latter, a new clique vector-space framework is introduced in this paper, where the vector space with a basis consisting of links has a dimension equal to the number of links, that with a basis consisting of triangles has the dimension equal to the number of triangles and so *** two vector spaces are related through a boundary operator, for example mapping the boundary of a triangle in one space to the sum of three links in the other *** the new framework,some important concepts and methodologies from algebraic topology, such as characteristic number,homology group and Betti number, will play a part in network science leading to foreseeable new research *** immediate applications, the paper illustrates some important characteristics affecting the collective behaviors of complex networks, some new cycle-dependent importance indexes of nodes and implications for network synchronization and brain-network analysis.

关键词： boundary operator clique vector space cycle homology group totally homogenous network

Pinning synchronization of networked multi-agent systems: spectral analysis

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Control Theory and Technology 2015年第1期13卷 45-54页

作者： Linying XIANG Fei chen guanrong chen Department of Automation Xiamen University Department of Electronic Engineering City University of Hong Kong

Pinning synchronization of a networked multi-agent system with a directed communication topology is investigated from a spectral analysis approach. Some new types of synchronized regions for networked systems with different nonlinear agent dynamics and inner coupling structures are discovered. The eigenvalue distributions of the coupling and control matrices for different types of directed networks are obtained. The effects of the network topology, pinning density and pinning strength on the network synchronizability are examined through extensive numerical simulations. It is shown that the synchronizability of the pinned network can be effectively improved by increasing pinning density and pinning strength for some types of synchronized regions, whereas too large the pinning density and pinning strength will lead to desynchronization for other types. It is found that directed random networks are not always easier to synchronize than directed small-world networks, and a denser eigenvalue distribution may not always imply better synchronizability.

关键词： Multi-agent system directed network pinning control spectral analysis synchronizability synchronized region

Dynamics and synchronization of a complex-valued star network

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Science China(Technological Sciences) 2021年第12期64卷 2729-2743页

作者： CHAI Lin LIU Jian chen guanrong ZHAO Xiu School of Mathematical Sciences University of JinanJinan 250022China Department of Electrical Engineering City University of Hong KongHong KongChina

Complex networks have been extensively investigated in recent ***,the dynamics,especially chaos and bifurcation,of the complex-valued complex network are rarely *** this paper,a star network of coupled complex-valued van der Pol oscillators is proposed to reveal the mechanism of star *** the aid of bifurcation diagram,Lyapunov exponent spectrum and phase portrait in this study,chaos,hyper-chaos,and multi-existing chaotic attractors are observed from the star network,although there are only periodic states in a complex-valued van der Pol *** versus coupling strength and nonlinear coefficient shows that the bigger the network size,the larger the parameter range within the chaotic(hyper-chaotic)*** is revealed that the chaotic bifurcation path is highly robust against the size variation of the star network,and it always evolves to chaos directly from period-1 and quasi-periodic states,***,the coexistence of chaotic phase synchronization and complete synchronization among the peripherals is also found from the star network,which is a symmetrybreaking phenomenon.

关键词： star network chaotic phase synchronization complex-valued van der Pol oscillator symmetry-breaking

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Enhancing Controllability Robustness of q-Snapback Networks through Redirecting Edges

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Research 2019年第1期2019卷 719-741页

作者： Yang Lou Lin Wang guanrong chen City University of Hong Kong Hong Kong Shanghai Jiao Tong University Shanghai 200240China

Te well-known small-world network model was established by randomly rewiring edges,aiming to enhance the synchronizability of an undirected nearest-neighbor regular *** paper demonstrates via extensive numerical simulations that randomly redirecting edges could enhance the robustness of the network controllability for directed snapback networks against both random and intentional node-removal and edge-removal attacks.

关键词： undirected directed neighbor