2,312 publications from this institution
Pinning control of a complex network aims at forcing the states of all nodes to track an external signal by controlling a small number of nodes in the network. In this paper, an algebraic graph-theoretic condition is introduced to optimize pinning control. When individual node dynamics and coupling strength of the network are given, the effectiveness of pinning scheme can be measured by the smallest eigenvalue of the grounded Laplacian matrix obtained by deleting the rows and columns corresponding to the pinned nodes from the Laplacian matrix of the network. The larger this smallest eigenvalue, the more effective the pinning scheme. Spectral properties of the smallest eigenvalue are analyzed using the network topology information, including the spectrum of the network Laplacian matrix, the minimal degree of uncontrolled nodes, the number of edges between the controlled node set and the uncontrolled node set, etc. The identified properties are shown effective for optimizing the pinning control strategy, as demonstrated by illustrative examples. Finally, for both scale-free and small-world networks, in order to maximize their corresponding smallest eigenvalues, it is better to pin the nodes with large degrees when the percentage of pinned nodes is relatively small, while it is better to pin nodes with small degrees when the percentage is relatively large. This surprising phenomenon can be explained by one of the theorems established.
Dynamical behavior of a new piecewise-linear continuous-time three-dimensional autonomous chaotic system is studied. System equilibria and their stabilities are discussed. Routes to chaos and bifurcations of the system are demonstrated with various numerical examples, where the chaotic features are justified numerically via computing the system fractal dimensions, Lyapunov exponents and power spectrum.
In this Letter, we show that it is impossible to uniformly and asymptotically stabilize a chaotic orbit (in the sense of the classical orbital stability) by using state feedback control, for both discrete and continuous autonomous systems, if the autonomous chaotic system has a continuous vector field and the controller is a continuous function of the system state. We draw this conclusion from our new result stating that once a bounded orbit is uniformly and asymptotically orbitally stabilized, it must become periodic or converge to a periodic orbit.
Recently, a necessary and sufficient condition for multivaluedness to be implicitly exhibited by counter-cascaded systems was presented. Subsequently, several systems that exhibit multivaluedness were reported. This brief interprets a general information transmission system as a counter-cascaded system with Shannon's noisy-channel coding theorem, providing a sufficient but not necessary condition for single-valuedness.
For the cantilever beam vibration model without damping and forced terms, the corresponding differential system is a planar dynamical system with some singular straight lines. In this paper, by using the techniques from dynamical systems and singular traveling wave theory developed by [ Li & Chen, 2007 ] to analyze its corresponding differential system, the bifurcations and the dynamical behaviors of the corresponding phase portraits are identified and analyzed. Under different parameter conditions, exact homoclinic and heteroclinic solutions, periodic solutions, compacton solutions, as well as peakons and periodic peakons, are all found explicitly.
A novel descriptor for invariant pattern recognition is proposed by using the Radon transform, the shift-invariant wavelet packet transform, and the Fourier transform. Experimental results show that the proposed descriptor achieves high recognition rates under different rotation angles and noise levels. It outperforms a previously developed method under the noisy environment.
No abstract is provided for this article.
In this article, a family of diffeomorphisms with growing horseshoes contained in global attracting regions is presented, where the dimension of the unstable direction can be any fixed integer and a growing horseshoe means that the number of the folds of the horseshoe is increasing as a parameter is varied. Moreover, it is demonstrated that the horseshoe-like attractors are observable for certain parameters.
No abstract is provided for this article.
This paper explores the state controllability of deep-coupling networks with inter-layer couplings, where the nodes of each layer are higher-dimensional linear time-invariant dynamical systems. The collective effects on the network controllability from intra-layer network topologies, node dynamics, external control inputs and inner interactions are extensively explored under two representative inter-layer coupling modes, where the integrated network can be controllable even if the intra-layer network topology is uncontrollable by external inputs. Some necessary and/or sufficient conditions for the network controllability are obtained for the representative two-layer intra-layer couplings of interdependent and drive-response modes. Simulated examples reveal the important role of inter-layer couplings of a controllable deep-coupling dynamical network assembled from uncontrollable intra-layer networks.
