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http://www.maths.qmul.ac.uk/%7Elatora/report_06.pdf

Complex networks: Structure and dynamics

We will review some of the major results in random graphs and some of the more challenging open problems. We will cover algorithmic and structural questions. We will touch on newer models, including those related to the WWW.

Random graphs

“Unpaired Image-to-Image Translation using Cycle-Consistent Adversarial Networks”の学習報告

Social Network Analysis

This note further investigates the locally and globally adaptive synchronization of an uncertain complex dynamical network. Several network synchronization criteria are deduced. Especially, our hypotheses and designed adaptive controllers for network synchronization are rather simple in form. It is very useful for future practical engineering design. Moreover, numerical simulations are also given to show the effectiveness of our synchronization approaches.

Adaptive synchronization of an uncertain complex dynamical network

Pinning adaptive synchronization of a general complex dynamical network

Over the last two decades, theoretical design and circuit implementation of various chaos generators have been a focal subject of increasing interest due to their promising applications in various ...

/pdf/generating-multiscroll-chaotic-attractors-theories-methods-16uxys4njg.pdf

Generating Multiscroll Chaotic Attractors: Theories, Methods and Applications

Many real-world complex networks display a small-world feature-a high degree of clustering and a small average distance. We show that the maximum synchronizability of a network is completely determined by its associated feedback system, which has a precise meaning in terms of synchronous communication. We introduce a new concept of synchronizability matrix to characterize the maximum synchronizability of a network. Several new concepts, such as sensitive edge and robust edge, are proposed for analyzing the robustness and fragility of synchronization of a network. Using the knowledge of synchronizability, we can purposefully increase the robustness of the network synchronization and prevent it from attacks. Some applications in small-world networks are also discussed briefly.

/pdf/characterizing-the-synchronizability-of-small-world-3d5letnnw8.pdf

Characterizing the synchronizability of small-world dynamical networks

Recently, it has been demonstrated that many large-scale complex dynamical networks display a collective synchronization motion. Here, we introduce a time-varying complex dynamical network model and further investigate its synchronization phenomenon. Based on this new complex network model, two network chaos synchronization theorems are proved. We show that the chaos synchronization of a time-varying complex network is determined by means of the inner coupled link matrix, the eigenvalues and the corresponding eigenvectors of the coupled configuration matrix, rather than the conventional eigenvalues of the coupled configuration matrix for a uniform network. Especially, we do not assume that the coupled configuration matrix is symmetric and its off-diagonal elements are nonnegative, which in a way generalizes the related results existing in the literature.

/pdf/chaos-synchronization-of-general-complex-dynamical-networks-41budoprfj.pdf

Jinhu Lu

Papers

Adaptive synchronization of an uncertain complex dynamical network

Pinning adaptive synchronization of a general complex dynamical network

Generating Multiscroll Chaotic Attractors: Theories, Methods and Applications

Characterizing the synchronizability of small-world dynamical networks

Chaos synchronization of general complex dynamical networks