Over the last decade, complex networks have emerged to be a promising research field in the area of circuits and systems. This mini-review paper introduces the special session that deals with theory and applications of complex networks and provides brief review of their advances and challenges. The paper further promotes some important research topics in the field with emphasis on the multidisciplinary research interests.
This paper is concerned with chaos of time-varying (i.e. non-autonomous) discrete systems in metric spaces. Some basic concepts are introduced for general time-varying systems, including periodic point, coupled-expansion for transitive matrix, uniformly topological equiconjugacy, and three definitions of chaos, i.e. chaos in the sense of Devaney and Wiggins, respectively, and in a strong sense of Li–Yorke. An interesting observation is that a finite-dimensional linear time-varying system can be chaotic in the original sense of Li–Yorke, but cannot have chaos in the strong sense of Li–Yorke, nor in the sense of Devaney in a set containing infinitely many points, and nor in the sense of Wiggins in a set starting from which all the orbits are bounded. A criterion of chaos in the original sense of Li–Yorke is established for finite-dimensional linear time-varying systems. Some basic properties of topological conjugacy are discussed. In particular, it is shown that topological conjugacy alone cannot guarantee two topologically conjugate time-varying systems to have the same topological properties in general. In addition, a criterion of chaos induced by strict coupled-expansion for a certain irreducible transitive matrix is established, under which the corresponding nonlinear system is proved chaotic in the strong sense of Li–Yorke. Two illustrative examples are finally provided with computer simulations for illustration. Keywords: time-varying discrete systemnonautonomous difference equationchaostopological conjugacycoupled-expansionAMS Subject Classifications: 37D4537B5537B10 Acknowledgements This research was supported by the NSF of Shandong Province (Grant Y1906A15) and the France-Hong Kong joint research scheme under the grant F-HK02/06T. The authors thank the referees for their valuable comments and suggestions.
The unified canonical feedback control strategy developed recently by the present authors for controlling chaotic systems is refined and applied to the well-known Chua's circuit, driving its orbits from the chaotic attractor to its unstable limit cycle. Simple sufficient conditions for the controllability of this particular circuit are established. Simulation results are included to visualize the control process. A circuit implementation of the designed feedback control is realized by adding a linear resistor and an appropriate periodic-signal generator to the original circuit.
A hybrid multi-agent systems model integrating the advantages of both metric interaction and topological interaction rules, called the metric-topological model, is developed. This model describes planar motions of mobile agents, where each agent can interact with all the agents within a circle of a constant radius, and can furthermore interact with some distant agents to reach a pre-assigned number of neighbors, if needed. Some sufficient conditions imposed only on system parameters and agent initial states are presented, which ensure achieving synchronization of the whole group of agents. It reveals the intrinsic relationships among the interaction range, the speed, the initial heading, and the density of the group. Moreover, robustness against variations of interaction range, density, and speed are investigated by comparing the motion patterns and performances of the hybrid metric-topological interaction model with the conventional metric-only and topological-only interaction models. Practically in all cases, the hybrid metric-topological interaction model has the best performance in the sense of achieving highest frequency of synchronization, fastest convergent rate, and smallest heading difference.
Recent studies suggest that circular RNA (circRNA)‐mediated post‐translational modification of RNA‐binding proteins (RBP) plays a pivotal role in metastasis of hepatocellular carcinoma (HCC). However, the specific mechanism and potential clinical therapeutic significance remain vague. This study attempts to profile the regulatory networks of circRNA and RBP using a multi‐omics approach. Has_circ_0006646 (circ0006646) is an unreported circRNA in HCC and is associated with a poor prognosis. Silencing of circ0006646 significantly hinders metastasis in vivo. Mechanistically, circ0006646 prevents the interaction between nucleolin (NCL) and the E3 ligase tripartite motif‐containing 21 to reduce the proteasome‐mediated degradation of NCL via K48‐linked polyubiquitylation. Furthermore, the change of NCL expression is proven to affect the phosphorylation levels of multiple proteins and inhibit p53 translation. Moreover, patient‐derived tumor xenograft and lentivirus injection, which is conducted to simulate clinical treatment confirmed the potential therapeutic value. Overall, this study describes the integrated multi‐omics landscape of circRNA‐mediated NCL ubiquitination degradation in HCC metastasis and provides a novel therapeutic target.
No abstract is provided for this article.
This paper shows that the maximum synchronizability of a general time-invariant dynamical network is completely determined by its associated internal feedback dynamics, which has a precise physical meaning in terms of synchronous communication. Also, a concept of synchronizability matrix is introduced to characterize the robustness of synchronization of the network. Based on the knowledge of synchronizability, we can purposefully increase the robustness of the network synchronization and better prevent it from attacks.
1 Department of Mathematics, Southeast University, Nanjing 210096, China 2 Faculty of Mathematics and Natural Sciences, ITM, University of Groningen, 9747 AG Groningen, The Netherlands 3 Department of Electronic Engineering, City University of Hong Kong, Hong Kong 4 School of Engineering and Information Technology, The University of New South Wales at ADFA, Canberra, ACT 2600, Australia 5 School of Electrical and Computer Engineering, RMIT University, Melbourne, VIC 3001, Australia
No abstract is provided for this article.
Based on analytic and numerical investigations of chaotic vibrations and quasiperiodic rotations of the Froude pendulum, we present a sufficient condition for controlling chaos by means of a weak resonant excitation as the initial phase difference Ψ varies. It is shown via the Melnikov function method that the initial phase difference Ψ plays a vital role in suppressing or inducing chaotic motions or quasiperiodic rotations.
This paper considers a second-order consensus problem for multiagent systems with nonlinear dynamics and directed topologies where each agent is governed by both position and velocity consensus terms with a time-varying asymptotic velocity. To describe the system's ability for reaching consensus, a new concept about the generalized algebraic connectivity is defined for strongly connected networks and then extended to the strongly connected components of the directed network containing a spanning tree. Some sufficient conditions are derived for reaching second-order consensus in multiagent systems with nonlinear dynamics based on algebraic graph theory, matrix theory, and Lyapunov control approach. Finally, simulation examples are given to verify the theoretical analysis.
This paper studies the following two-dimensional nonlinear partial difference systems T(∇1,∇2)(xmn)+bmng(ymn)=0, T(Δ1,Δ2)(ymn)+amnf(xmn)=0, where m,n∈N 0={0,1,2,…}, T(Δ 1,Δ 2)=Δ 1+Δ 2+I, T(∇1,∇2)=∇1+∇2+I, Δ 1 y mn =y m+1,n −y mn , Δ 2 y mn =y m,n+1−y mn , Iy mn =y mn , ∇1 y mn =y m−1,n −y mn , ∇2 y mn =y m,n−1−y mn , {a mn } and {b mn } are real sequences, m,n∈N 0, and f,g:R→R are continuous with uf(u)>0 and ug(u)>0 for all u≠0. A solution ({x mn },{y mn }) of the system is oscillatory if both components are oscillatory. Some sufficient conditions for all solutions of this system to be oscillatory are derived.
