2,312 publications from this institution
A simple, yet mathematically rigorous feedback control design method is proposed in this paper, which can make all the Lyapunov exponents of the controlled system strictly positive, for any given n-dimensional dynamical system that could be originally nonchaotic or even asymptotically stable. The argument used is purely algebraic and the design procedure is completely schematic, with no approximations used throughout the derivation. This is a rigorous and convenient technique suggested as an attempt for anticontrol of chaotic dynamical systems, with explicit computational formulas derived for applications.
Cross-border equity and long-term debt securities portfolio investment networks are analysed from 2002 to 2012, covering the 2008 global financial crisis. They serve as network-proxies for measuring the robustness of the global financial system and the interdependence of financial markets, respectively. Two early-warning indicators for financial crises are identified: First, the algebraic connectivity of the equity securities network, as a measure for structural robustness, drops close to zero already in 2005, while there is an over-representation of high-degree off-shore financial centres among the countries most-related to this observation, suggesting an investigation of such nodes with respect to the structural stability of the global financial system. Second, using a phenomenological model, the edge density of the debt securities network is found to describe, and even forecast, the proliferation of several over-the-counter-traded financial derivatives, most prominently credit default swaps, enabling one to detect potentially dangerous levels of market interdependence and systemic risk.
A systematic circuit design approach is proposed for experimental verification of hyperchaotic 2-, 3-, 4-scroll attractors from a generalized Matsumoto–Chua–Kobayashi (MCK) circuit. Moreover, using appropriate discrete and extended transformations, a novel digital signal processor (DSP) method is also presented for physically realizing the above hyperchaotic 2-, 3-, 4-scroll attractors. This is the first time in the literature to report the experimental verification of hyperchaotic 3- and 4-scroll attractors. Some recursive formulas of system parameters are rigorously derived, useful for improving circuit implementation.
Distributed consensus tracking is addressed in this paper for multi-agent systems with Lipschitz-type node dynamics. The main contribution of this work is solving the consensus tracking problem without the assumption that the topology among followers is strongly connected and fixed. By using tools from M-matrix theory, a class of consensus tracking protocols based only on the relative states among neighboring agents is designed. By appropriately constructing Lyapunov function, it is proved that consensus tracking in the closed-loop multi-agent systems with a fixed topology having a directed spanning tree can be achieved if the feedback gain matrix and the coupling strength are suitably selected. Furthermore, with the assumption that each possible topology contains a directed spanning tree, it is theoretically shown that consensus tracking under switching directed topologies can be achieved if the control parameters are suitably selected and the dwell time is larger than a positive threshold. The results are then extended to the case where the communication topology contains a directed spanning tree only frequently as the system evolves with time. Finally, some numerical simulations are given to verify the theoretical analysis.
No abstract is provided for this article.
A very simple and efficient algorithm is formulated for reducing any transfer function to its coprime form without long divisions.
No abstract is provided for this article.
Deflection routing is a mechanism to route packets away from congestion. Traditional shortest path routing uses only the static topological information as input, whereas deflection routing takes into account the dynamic queue length information. In the simplest form of deflection routing, a packet being dropped due to queue buffer overflow is "rescued" and is rerouted to other links. Deflection routing can thus reduce the rate of packet drops and allow a network to carry more packets without the need of additional bandwidth. However, it can also lead to unstable deflecting behavior in some congestion scenario. It is important to study deflection behavior when operating near the point of congestion. In this paper, the performance in terms of packet drop rate and traveling time are studied through extensive simulation, and complex behavior in the traffic with self-similarity property is observed and discussed.
This article addresses some new problems and challenges faced by the conventional control theory under complex dynamical network environments. After introducing the network science and engineering background, it discusses some research issues regarding pinning control of complex dynamical networks, controllability of directed networks, as well as “network of networks” and its modeling and control.
Let $f$ be a continuous self-map on a compact interval $I$ and $\hat f$ be the induced map on the space $\mathcal{M}(I)$ of probability measures. We obtain a sharp condition to guarantee that $(I,f)$ is transitive if and only if $(\mathcal{M}(I),\hat f)$ is transitive. We also show that the sensitivity of $(I,f)$ is equivalent to that of $(\mathcal{M}(I),\hat f)$. We prove that $(\mathcal{M}(I),\hat f)$ must have infinite topological entropy for any transitive system $(I,f)$, while there exists a transitive non-autonomous system $(I,f_{0,\infty})$ such that $(\mathcal{M}(I),\hat f_{0,\infty})$ has zero topological entropy, where $f_{0,\infty}=\{f_n\}_{n=0}^\infty$ is a sequence of continuous self-maps on $I$. For a continuous self-map $f$ on a general compact metric space $X$, we show that chain transitivity of $(X, f)$ implies chain mixing of $(\mathcal{M}(X),\hat f)$, and we provide two counterexamples to demonstrate that the converse is not true. We confirm that shadowing of $(X,f)$ is not inherited by $(\mathcal{M}(X),\hat f)$ in general. For a non-autonomous system $(X,f_{0,\infty})$, we prove that Li-Yorke chaos (resp., distributional chaos) of $(X,f_{0,\infty})$ carries over to $(\mathcal{M}(X),\hat f_{0,\infty})$, and give an example to show that the converse may not be true. We prove that if $f_n$ is surjective for all $n\geq 0$, then chain mixing of $(\mathcal{M}(X),\hat f_{0,\infty})$ always holds true, and shadowing of $(\mathcal{M}(X),\hat f_{0,\infty})$ implies topological mixing of $(X, f_{0,\infty})$. In addition, we prove that topological mixing (resp., mild mixing and topological exactness) of $(X, f_{0,\infty})$ is equivalent to that of $(\mathcal{M}(X),\hat f_{0,\infty})$, and that $(X, f_{0,\infty})$ is cofinitely sensitive if and only if $(\mathcal{M}(X),\hat f_{0,\infty})$ is cofinitely sensitive.
In this paper, we provide a statistical analysis for the Lyapunov exponents estimated from time series. Through the Jacobian estimation approach, the asymptotic distributions of the estimated Lyapunov exponents of discrete-time dynamical systems are studied and characterized based on the time series. Some new results under weak conditions are obtained. The theoretical results presented in the paper are illustrated by numerical simulations.
