两个网络间的相互同步

本文研究了两个耦合网络的相互同步,利用线性化方法,我们给出了两个具有相同拓扑结构的网络实现同步的定理,最后用数值例子来验证得到的理论结果。     

脉冲控制下复杂网络的同步

主要考虑非对称耦合复杂网络的脉冲同步问题.通过构造Lyapunov泛函,设计合适的脉冲控制器,并利用时滞脉冲系统理论,给出了网络脉冲同步新的判别准则.数值模拟表明所得结果是正确的.     

Call Admission: A New Approach to Quality of Service

Quality of service guarantees are an important and much discussed aspect of ATM network design. However, there is no standard definition of quality of service. Moreover, some often-used criteria seem quite crude. We consider call admission to a bufferless ATM multiplexer with on/off sources. A new criterion for a guarantee on average cell loss is proposed. This criterion represents the quality of service from the point of view of the user, and is thus more reliable. We calculate the optimal policy that minimizes blocking subject to the guarantee, when there is only one type of user.The measure of cell-loss we propose is applicable to a wide range of models. It gives rise to a mathematical programming formulation, which we derive explicitly for our case.     

Complete Distributivity of Lattice Ordered Groups and of Vector Lattices

In this paper we investigate the possibility of a regular embedding of a lattice ordered group into a completely distributive vector lattice.     

Generalized function projective (lag, anticipated and complete) synchronization between two different complex networks with nonidentical nodes

Generalized function projective (lag, anticipated and complete) synchronization between two different complex networks with nonidentical nodes is investigated in this paper. Based on Barbalat’s lemma, some sufficient synchronization criteria are derived by applying the nonlinear feedback control. Although previous work studied function projective synchronization on complex dynamical networks, the dynamics of the nodes are coupled partially linear chaotic systems. In our work, the dynamics of the nodes of the complex networks are any chaotic systems without the limitation of the partial linearity. In addition, each network can be undirected or directed, connected or disconnected, and nodes in either network may have identical or different dynamics. The proposed strategy is applicable to almost all kinds of complex networks. Numerical simulations further verify the effectiveness and feasibility of the proposed synchronization method. Numeric evidence shows that the synchronization rate is sensitively influenced by the feedback strength, the time delay, the network size and the network topological structure.     

Projective synchronization of different fractional-order chaotic systems with non-identical orders

This paper investigates the projective synchronization (PS) of different fractional order chaotic systems while the derivative orders of the states in drive and response systems are unequal. Based on some essential properties on fractional calculus and the stability theorems of fractional-order systems, we propose a general method to achieve the PS in such cases. The fractional operators are introduced into the controller to transform the problem into synchronization problem between chaotic systems with identical orders, and the nonlinear feedback controller is proposed based on the concept of active control technique. The method is both theoretically rigorous and practically feasible. We present two examples that illustrate the effectiveness and applications of the method, which include the PS between two 3-D commensurate fractional-order chaotic systems and the PS between two 4-D fractional-order hyperchaotic systems with incommensurate and commensurate orders, respectively. Abundant numerical simulations are given which agree well with the analytical results. Our investigations show that PS can also be achieved between different chaotic systems with non-identical orders. We have further reviewed and compared some relevant methods on this topic reported in several recent papers. A discussion on the physical implementation of the proposed method is also presented in this paper.     

Generalized synchronization of two bidirectionally coupled discrete dynamical systems

Based on the modified system approach the generalized synchronization (GS) in two bidirectionally coupled discrete dynamical systems is classified into several types, and under some conditions, the existence, Lipschitz smoothness and Hölder continuity of two kinds of GS therein are derived and theoretically proved. In addition, numerical simulations validate the present theory.     

Refinement of Vahlen's Theorem for Minkowski Bases of Three-Dimensional Lattices

In the paper, the analog of Vahlen's theorem for Minkowski bases of three-dimensional lattices is sharpened.     

Chaotic Numbers of Complete Bipartite Graphs and Tripartite Graphs

In this paper, we study the chaotic numbers of complete bipartite graphs and complete tripartite graphs. For the complete bipartite graphs, we find closed-form formulas of the chaotic numbers and characterize all chaotic mappings. For the complete tripartite graphs, we develop an algorithm running in O(n ⁴ ₃) time to find the chaotic numbers, with n ₃ the number of vertices in the largest partite set.Research supported by NSC 90-2115-M-036-003.The author thanks the authors of Ref. 6, since his work was motivated by their work. Also, the author thanks the referees for helpful comments which made the paper more readable.     

On some bidimensional denumerable chains of infinite order

We study homogeneous chains of infinite order (ξ_t)_{t∈$\text{Z}$} with the set of states taken to be $\text{X=(}\text{N}\text{{0,1})x{-1,1}}$. Our approach is to interpret the half-infinite sequence ..., ξ_?n,..., ξ_?1, ξ₀, where $\text{ξ}{}_{\mathrm{t}}\text{=(i}{}_{\mathrm{t}}\text{, ε}{}_{\mathrm{t}}\text{) ∈ X, t ∈}\text{Z}$ as the continued fraction to the nearer integer expansion (read inversely) of a y ? [?$\text{1}\text{2}$,$\text{1}\text{2}$]. Thus, we are led to study certain Y-valued Markov chains, where Y = [?$\text{1}\text{2}$, $\text{1}\text{2}$] and then by making use of their properties we establish the existence of denumerable chains of infinite order under conditions different from those given in Theorem 2.3.8 of Iosifescu-Theodorescu (1969). A (weak) variant of mixing is proved as well.