Publications

Control of beam halo-chaos has been a very challenging subject for research in recent years, in which some nonlinear feedback methods have been developed for suppression of beam halo-chaos in high-current proton linear accelerators. However, stability analysis of such successful nonlinear feedback control methods has not yet been rigorously carried out, which remains an important open topic in the field. In this letter, we present a rigorous mathematical analysis of several nonlinear feedback control methods that are applied to control beam halo-chaos with great success on simulations.

This paper provides a case study of a two-dimensional area-preserving non-hyperbolic chaotic map, revealing to some new phenomena that have not been well discussed in the literature to date.

A robust Kalman filtering (KF) algorithm based on the evolutionary programming (EP) technique is proposed in this paper, for uncertain systems with unknown-but-bounded uncertain parameters which are described by interval systems. This algorithm takes advantage of the global optima-searching capability of EP to find the optimal KF results at every iteration, which include both the upper–lower boundaries and the nominal trajectory of the optimal estimates of the system state vectors. One prominent feature of this EP filtering algorithm is that it assumes the same statistical conditions and provides the same optimal estimates as the conventional KF scheme. Both linear and nonlinear systems are studied. Two typical computer simulation examples are given with comparison, which verify the merits of the new method – it yields more accurate estimation results and is less conservative as compared to the existing interval Kalman filtering (IKF).

obtained, improving the main results in [Q.

Consider the following two spatially generalized Logistic systems: xm+1,n+ωxm,n+1=1−μ1[(1+ω)xmn]2 and ym+1,n+ωym,n+1=1−μ2[(1+ω)ymn]2, where ω is a real constant, and μ 1 and μ 2 are two real parameters. An analytical method is introduced for generalized synchronization of these two spatially chaotic systems, and a range of the coupling constant is specified for the generalized synchronization. Moreover, a nonlinear function is characterized for synchronization stability of the two coupled systems.

In this paper, we describe certain techniques for mapping the modified extended Kalman filter (MEKF) onto systolic array processors. First, we introduce a square-root algorithm based on the singular value decomposition (SVD) for the Kalman filter. Then, we develop a VLSI architecture of the systolic array type for its implementation. Compared with other existing square-root Kalman filtering algorithms, our new design is numerically more stable and has nicer parallel and pipelining characteristics when it is applied to the MEKF. Moreover, it achieves higher efficiency. For n-dimensional state vector estimations, the proposed architecture consists of O(3/2n 2) processing elements and completes an iteration in time O((s + 8)n), in contrast to the time complexity of O((s + 3)n 3) for a sequential implementation, where s ≈ log n.

This paper proves that a set-valued dynamical system is sensitively dependent on initial conditions (resp., $\mathscr{F}$-sensitive, multi-sensitive) if and only if its $g$-fuzzification is sensitively dependent on initial conditions (resp., $\mathscr{F}$-sensitive, multi-sensitive), where $\mathscr{F}$ is a Furstenberg family. As an application, it is shown that there exists a sensitive dynamical system whose $g$-fuzzification does not have such sensitive dependence for any $g$ in a certain domain. Moreover, a sufficient condition ensuring that the $g$-fuzzification of every nontrivial dynamical system is not transitive is obtained. These give an answer to a question posed in \cite[J. Kupka, Information Sciences, {\bf 279} (2014): 642--653]{Kupka2014}.

In this paper, a shallow water wave model is used to introduce the concepts of peakon, periodic peakon and compacton. Traveling wave solutions of the shallow water equation are presented. The corresponding traveling wave system is a singular planar dynamical system with one singular straight line. By using the method of dynamical systems, bifurcation diagrams and explicit exact parametric representations of the solutions are given, including solitary wave solution, periodic wave solution, peakon solution, periodic peakon solution and compacton solution under different parameter conditions.

Recently a great deal of effort has been made to explicitly determine the mean first-passage time (MFPT) between two nodes averaged over all pairs of nodes on a fractal network. In this paper, we first propose a family of generalized delayed recursive trees characterized by two parameters, where the existing nodes have a time delay to produce new nodes. We then study the MFPT of random walks on this kind of recursive tree and investigate the effect of the time delay on the MFPT. By relating random walks to electrical networks, we obtain an exact formula for the MFPT and verify it by numerical calculations. Based on the obtained results, we further show that the MFPT of delayed recursive trees is much shorter, implying that the efficiency of random walks is much higher compared with the non-delayed counterpart. Our study provides a deeper understanding of random walks on delayed fractal networks.

This paper investigates the impact of edge-adding number m and edge-adding distance d on both synchronizability and average path length of NW small-world networks generated from ring networks via random edge-adding. It is found that the synchronizability of the network as a function of the distance d is fluctuant and there exist some d that have almost no impact on the synchronizability and may only scarcely shorten the average path length of the network. Numerical simulations on a network of Lorenz oscillators confirm the above results. This phenomenon shows that the contributions of randomly added edges to both the synchronizability and the average path length are not uniform nor monotone in building an NW small-world network with equal-distance edge additions, implying that only if appropriately adding edges when building up the NW small-word network can help enhance the synchronizability and/or reduce the average path length of the resultant network. Finally, it is shown that this NW small-world network has worse synchronizability and longer average path length, when compared with the conventional NW small-world network, with random-distance edge additions. This may be due to the fact that with equal-distance edge additions, there is only one shortcut distance for better information exchange among nodes and for shortening the average path length, while with random-distance edge additions, there exist many different distances for doing so.

The response of energy envelop in complex nonlinear oscillator networks to stochastic excitations is studied. First, by using the stochastic averaging method for quasi-nonintegrable-Hamiltonian systems, the averaged Fokker–Planck– Kolmogorov equation governing the probability density of the Hamiltonian is established. Then, the stationary probability density of the Hamiltonian is derived, and the stationary probability density of the averaged energy as well as the statistical moments of the Hamiltonian is obtained. To that end, an illustrative example is provided with the analytical relationship between the response and the network parameters as well as the network structure. Specific solutions are presented for five representative topological structures. Throughout extensive simulations, the effects of system parameters, such as the network size, coupling strength and intensities of stochastic excitations on the response of the energy envelop of the networks, are carefully observed and analyzed.