SOME DYNAMICAL PROPERTIES OF THE UNIVERSAL UNFOLDING OF PITCHFORK

From the point of view of dynamics,the phenomenon of mode jumpingin the imperfect pitchfork problem is discussed.The dynamical mechanism of modeljumping of structures,such as plate and shell,that is brought about by the extremurninstability,is explained.Finally,we give numerical simulation to show the validity ofour results.     

On non-strong jumping numbers and density structures of hypergraphs

Estimating Turán densities of hypergraphs is believed to be one of the most challenging problems in extremal set theory. The concept of ‘jump’ concerns the distribution of Turán densities. A number α∈[0,1) is a jump for r-uniform graphs if there exists a constant c>0 such that for any family F of r-uniform graphs, if the Turán density of F is greater than α, then the Turán density of F is at least α+c. A fundamental result in extremal graph theory due to Erd?s and Stone implies that every number in [0,1) is a jump for graphs. Erd?s also showed that every number in [0,r!/r^r) is a jump for r-uniform hypergraphs. Furthermore, Frankl and Rödl showed the existence of non-jumps for hypergraphs. Recently, more non-jumps were found in [r!/r^r,1) for r-uniform hypergraphs. But there are still a lot of unknowns regarding jumps for hypergraphs. In this paper, we propose a new but related concept-strong-jump and describe several sequences of non-strong-jumps. It might help us to understand the distribution of Turán densities for hypergraphs better by finding more non-strong-jumps.     

Mode interaction in triple-bay prestressed stayed columns

Prestressed stayed columns are an innovative type of structural system where the compressive load-carrying capacity can be enhanced through prestressed external cable stays. A nonlinear analytical model for prestressed stayed columns with multiple crossarm systems along the column length, based on the Rayleigh–Ritz method, is presented that captures modal interactions for perfect geometries explicitly for the first time. It is demonstrated that the theoretical compressive strength enhancements under certain configurations can only be obtained at the expense of triggering a sequence of destabilizing bifurcations. This can give rise to dangerously unstable interactive post-buckling behaviour including so-called ‘mode jumping’ and ‘snaking’ phenomena. Parametric spaces where the system is most susceptible to the modal interactions are identified and it is for those configurations that the system is likely to be highly sensitive to initial imperfections. The model is validated using a nonlinear finite element model formulated within the commercial code ABAQUS and excellent comparisons are obtained.     

Robust stability analysis of stochastic neural networks with Markovian jumping parameters and probabilistic time‐varying delays

This article discusses the issue of robust stability analysis for a class of Markovian jumping stochastic neural networks (NNs) with probabilistic time‐varying delays. The jumping parameters are represented as a continuous‐time discrete‐state Markov chain. Using the stochastic stability theory, properties of Brownian motion, the information of probabilistic time‐varying delay, the generalized Ito's formula, and linear matrix inequality (LMI) technique, some novel sufficient conditions are obtained to guarantee the stochastical stability of the given NNs. In particular, the activation functions considered in this article are reasonably general in view of the fact that they may depend on Markovian jump parameters and they are more general than those usual Lipschitz conditions. The main features of this article are described in the following: first one is that, based on generalized Finsler lemma, some improved delay‐dependent stability criteria are established and the second one is that the nonlinear stochastic perturbation acting on the system satisfies a class of Lipschitz linear growth conditions. By resorting to the Lyapunov–Krasovskii stability theory and the stochastic analysis tools, sufficient stability conditions are established using an efficient LMI approach. Finally, two numerical examples and its simulations are given to demonstrate the usefulness and effectiveness of the proposed results. © 2014 Wiley Periodicals, Inc. Complexity 21: 59–72, 2016     

Exponential stability results for uncertain neutral systems with interval time-varying delays and Markovian jumping parameters

This paper deals with the global exponential stability analysis of neutral systems with Markovian jumping parameters and interval time-varying delays. The time-varying delay is assumed to belong to an interval, which means that the lower and upper bounds of interval time-varying delays are available. A new global exponential stability condition is derived in terms of linear matrix inequality (LMI) by constructing new Lyapunov-Krasovskii functionals via generalized eigenvalue problems (GEVPs). The stability criteria are formulated in the form of LMIs, which can be easily checked in practice by Matlab LMI control toolbox. Two numerical examples are given to demonstrate the effectiveness and less conservativeness of the proposed methods.     

Stability analysis of the differential genetic regulatory networks model with time-varying delays and Markovian jumping parameters

In this paper, we investigate the stability and robust stability criteria for genetic regulatory networks with interval time-varying delays and Markovian jumping parameters. The genetic regulatory networks have a finite number of modes, which may jump from one mode to another according to the Markov process. By using Lyapunov–Krasovskii functional, some sufficient conditions are derived in terms of linear matrix inequalities to achieve the global asymptotic stability in the mean square of the considered genetic regulatory networks. Two numerical examples are provided to illustrate the usefulness of the obtained theoretical results.     

Gregarious versus individualistic behavior in Vicsek swarms and the onset of first-order phase transitions

The standard Vicsek model (SVM) is a minimal non-equilibrium model of self-propelled particles that appears to capture the essential ingredients of critical flocking phenomena. In the SVM, particles tend to align with each other and form ordered flocks of collective motion; however, perturbations controlled by a noise term lead to a noise-driven continuous order–disorder phase transition. In this work, we extend the SVM by introducing a parameter α$\alpha$ that allows particles to be individualistic instead of gregarious, i.e. to choose a direction of motion independently of their neighbors. By focusing on the small-noise regime, we show that a relatively small probability of individualistic motion (around 10%$10\%$) is sufficient to drive the system from a Vicsek-like ordered phase to a disordered phase. Despite the fact that the α$\alpha$-extended model preserves the O(n)$O\left(n\right)$ symmetry and the interaction range, as well as the dimensionality of the underlying SVM, this novel phase transition is found to be discontinuous (first order), an intriguing manifestation of the richness of the non-equilibrium flocking/swarming phenomenon.     

An efficient numerical scheme for precise time integration of a diffusion-dissolution/precipitation chemical system

A numerical scheme based on an operator splitting method and a dense output event location algorithm is proposed to integrate a diffusion-dissolution/precipitation chemical initial-boundary value problem with jumping nonlinearities. The numerical analysis of the scheme is carried out and it is proved to be of order 2 in time. This global order estimate is illustrated numerically on a test case.

     

桥随路降法治理桥头跳车

分析软土地基上路堤与桥梁的沉降差异及跳车的原因,采用桥随路降的治理方法,应用柱式升降桥墩来调控桥面高程,使桥面降落高度与路面沉降量一致,保持道路竖曲线顺畅,消除桥头跳车.