Biological experimental demonstration of bifurcations from bursting to spiking predicted by theoretical models

A series of bifurcations from period-1 bursting to period-1 spiking in a complex (or simple) process were observed with increasing extra-cellular potassium concentration during biological experiments on different neural pacemakers. This complex process is composed of three parts: period-adding sequences of burstings, chaotic bursting to chaotic spiking, and an inverse period-doubling bifurcation of spiking patterns. Six cases of bifurcations with complex processes distinguished by period-adding sequences with stochastic or chaotic burstings that can reach different bursting patterns, and three cases of bifurcations with simple processes, without the transition from chaotic bursting to chaotic spiking, were identified. It reveals the structures closely matching those simulated in a two-dimensional parameter space of the Hindmarsh–Rose model, by increasing one parameter \(I\) and fixing another parameter \(r\) at different values. The experimental bifurcations also resembled those simulated in a physiologically based model, the Chay model. The experimental observations not only reveal the nonlinear dynamics of the firing patterns of neural pacemakers but also provide experimental evidence of the existence of bifurcations from bursting to spiking simulated in the theoretical models.     

Trapping in dendrimers and regular hyperbranched polymers

Dendrimers and regular hyperbranched polymers are two classic families of macromolecules, which can be modeled by Cayley trees and Vicsek fractals, respectively. In this paper, we study the trapping problem in Cayley trees and Vicsek fractals with different underlying geometries, focusing on a particular case with a perfect trap located at the central node. For both networks, we derive the exact analytic formulas in terms of the network size for the average trapping time (ATT)-the average of node-to-trap mean first-passage time over the whole networks. The obtained closed-form solutions show that for both Cayley trees and Vicsek fractals, the ATT display quite different scalings with various system sizes, which implies that the underlying structure plays a key role on the efficiency of trapping in polymer networks. Moreover, the dissimilar scalings of ATT may allow to differentiate readily between dendrimers and hyperbranched polymers.     

Jittering performance of random deflection routing in packet networks

This paper reports a study of random deflection routing protocol and its impact on delay-jitter over packet networks. In case of congestion, routers with a random deflection routing protocol can forward incoming packets to links laying off shortest paths; namely, packets can be “deflected” away from their original paths. However, random deflection routing may send packets to several different paths, thereby introducing packet re-ordering. This could affect the quality of receptions, it could also impair the overall performance in transporting data traffic. Nevertheless, the present study reveals that deflection routing could actually reduce delay-jitter when the traffic loading on the network is not heavy.     

Stimulus-induced transition of clustering firings in neuronal networks with information transmission delay

We propose a conceptually novel method of reconstructing the topology of dynamical networks. By examining the correlation between the variable of one node and the derivative of another node’s variable, we derive a simple matrix equation yielding the network adjacency matrix. Our assumptions are the possession of time series describing the network dynamics, and the precise knowledge of the internal interaction functions. Our method involves a tunable parameter, allowing for the reconstruction precision to be optimized within the constraints of given dynamical data. The method is illustrated on a simple example, and the dependence of the reconstruction precision on the dynamical properties of time series is discussed. Our theory is in principle applicable to any weighted or directed network whose interaction functions are known.     

Influence of inerter on natural frequencies of vibration systems

This paper investigates the influence of inerter on the natural frequencies of vibration systems. First of all, the natural frequencies of a single-degree-of-freedom (SDOF) system and a two-degree-of-freedom (TDOF) system are derived algebraically and the fact that the inerter can reduce the natural frequencies of these systems is demonstrated. Then, to further investigate the influence of inerter in a general vibration system, a multi-degree-of-freedom system (MDOF) is considered. Sensitivity analysis is performed on the natural frequencies and mode shapes to demonstrate that the natural frequencies of the MDOF system can always be reduced by increasing the inertance of any inerter. The condition for a general MDOF system of which the natural frequencies can be reduced by an inerter is also derived. Finally, the influence of the inerter position on the natural frequencies is investigated and the efficiency of inerter in reducing the largest natural frequencies is verified by simulating a six-degree-of-freedom system, where a reduction of more than 47 percent is obtained by employing only five inerters.     

Coupled-expanding maps and one-sided symbolic dynamical systems

This paper studies relationships between coupled-expanding maps and one-sided symbolic dynamical systems. The concept of coupled-expanding map is extended to a more general one: coupled-expansion for a transitive matrix. It is found that the subshift for a transitive matrix is strictly coupled-expanding for the matrix in certain disjoint compact subsets; the topological conjugacy of a continuous map in its compact invariant set of a metric space to a subshift for a transitive matrix has a close relationship with that the map is strictly coupled-expanding for the matrix in some disjoint compact subsets. A certain relationship between strictly coupled-expanding maps for a transitive matrix in disjoint bounded and closed subsets of a complete metric space and their topological conjugacy to the subshift for the matrix is also obtained. Dynamical behaviors of subshifts for irreducible matrices are then studied and several equivalent statements to chaos are obtained; especially, chaos in the sense of Li–Yorke is equivalent to chaos in the sense of Devaney for the subshift, and is also equivalent to that the domain of the subshift is infinite. Based on these results, several new criteria of chaos for maps are finally established via strict coupled-expansions for irreducible transitive matrices in compact subsets of metric spaces and in bounded and closed subsets of complete metric spaces, respectively, where their conditions are weaker than those existing in the literature.     

Generating chaos with a switching piecewise-linear controller

This paper introduces a new chaos generator, a switching piecewise-linear controller, which can create chaos from a three-dimensional linear system within a wide range of parameter values. Basic dynamical behaviors of the chaotic controlled system are investigated in some detail. (c) 2002 American Institute of Physics.     

Chaotic Vibrations of the One-Dimensional Wave Equation Due to a Self-Excitation Boundary Condition Part I: Controlled hysteresis

The study of nonlinear vibrations/oscillations in mechanical and electronic systems has always been an important research area. While important progress in the development of mathematical chaos theory has been made for finite dimensional second order nonlinear ODEs arising from nonlinear springs and electronic circuits, the state of understanding of chaotic vibrations for analogous infinite dimensional systems is still very incomplete.

The 1-dimensional vibrating string satisfying on the unit interval is an infinite dimensional harmonic oscillator. Consider the boundary conditions: at the left end , the string is fixed, while at the right end , a nonlinear boundary condition , takes effect. This nonlinear boundary condition behaves like a van der Pol oscillator, causing the total energy to rise and fall within certain bounds regularly or irregularly. We formulate the problem into an equivalent first order hyperbolic system, and use the method of characteristics to derive a nonlinear reflection relation caused by the nonlinear boundary condition. Since the solution of the first order hyperbolic system depends completely on this nonlinear relation and its iterates, the problem is reduced to a discrete iteration problem of the type , where is the nonlinear reflection relation. We say that the PDE system is chaotic if the mapping is chaotic as an interval map. Algebraic, asymptotic and numerical techniques are developed to tackle the cubic nonlinearities. We then define a rotation number, following J.P. Keener , and obtain denseness of orbits and periodic points by either directly constructing a shift sequence or by applying results of M.I. Malkin to determine the chaotic regime of for the nonlinear reflection relation , thereby rigorously proving chaos. Nonchaotic cases for other values of are also classified. Such cases correspond to limit cycles in nonlinear second order ODEs. Numerical simulations of chaotic and nonchaotic vibrations are illustrated by computer graphics.

     

复杂网络及其新近研究进展简介

简单地介绍了近10年来蓬勃发展的复杂网络研究新领域, 特别是其中最具代表性的随机网络、小世界网络和无尺度网络模型及其基本参数和概念, 并简要地回顾了复杂网络理论在生物和大脑神经网络、流行病传播与免疫控制、交通与社会经济、无线通讯、计算机和互联网、传感器网络、语言学与社会科学以及群体活动和编队飞行问题中的分散控制、稳定性特别是一致性问题等方面的应用趋势.     

4-氟-1,2-二氢-3,6-哒嗪二酮及其衍生物的合成

本文报导了4-氟-1,2-二氢-3,6-哒嗪二酮(Ⅱ)及其衍生物3,6-二氯-4-氟哒嗪(Ⅲ)、3-甲氧基-4-氟-6-氯哒嗪(Ⅳ)、3-邻甲苯氧基-4-氟-6-氯哒嗪(Ⅵ)、1-苯基-3-羟基-4-氟-6-哒嗪酮(Ⅶ)等五种新化合物的合成,探讨了(Ⅲ)同亲核试剂的反应性能和部分化合物的药理实验结果.