On the three-dimensional undulation instability of a rectangular viscoelastic composite plate in biaxial compression

Within the frame work of the second version of small precritical deformation in the three-dimensional linearized theory of stability of deformable bodies (TDLTSDB), the undulation instability problem for a simply supported rectangular plate made of a viscoelastic composite material is investigated in biaxial compression in the plate plane. The corresponding boundary-value problem is solved by employing the Laplace transformation and the principle of correspondence. For comparison and estimation of the accuracy of results given by the TDLTSDB, the same problem is also solved by using various approximate plate theories. The viscoelasticity properties of the plate material are described by the Rabotnov fractional-exponential operator. The numerical results and their discussion are presented for the case where the plate is made of a multilayered viscoelastic composite material. In particular, the variation range of problem parameters is established for which it is necessary to investigate the undulation instability of the viscoelastic composite plate by using the TDLTSDB. Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 45, No. 1, pp. 93–108, January–February, 2009.     

Lower bounds of the topological entropy for nonautonomous dynamical systems

In this paper, lower bounds of the topological entropy for nonautonomous dynamical systems are given via the growths of topological complexity in fundamental group and in degree.     

离散Leslie—Gower型捕食与被捕食系统的Neimark—Sacker分岔

本文利用映射的分岔理论讨论了离散Leslie—Gower型捕食与被捕食系统的Neimark—Sacker分岔,并通过数值模拟验证了所得结果的正确性。     

一类离散的Holling-I型捕食与被捕食系统的Flip分岔

本文利用中心流形定理和映射的分岔理论,研究了一类离散的捕食与被捕食系统的倍周期分岔的存在性与稳定性。     

Self-similarity of electrostatic fluctuations in a linear magnetised plasma system

In this Letter the long-range time correlations present in the fluctuation data in presence of electrostatic instability in a magnetised dc discharge plasma is presented. The electrostatic instability is generated due to the effect of crossed electric and magnetic field (E×B flow) and has intermediate frequency ranging from 50 to 100 MHz. Hurst exponent, the self-similarity parameter is calculated with the help of different statistical methods suggested by many researchers to determine the long-range time correlation present in fluctuation dynamics in the plasma column. The fluctuation in the ion saturation current is measured by a Langmuir probe for the study and the measurement is done both radially and axially in the plasma system. Estimated results clearly expose the self-similar character of the fluctuations with self-similarity parameters having values from 0.65 to 0.90 through the presence of long-range time correlation.     

Chaotic dynamics of a third-order Newton-type method

The dynamics of a classical third-order Newton-type iterative method is studied when it is applied to degrees two and three polynomials. The method is free of second derivatives which is the main limitation of the classical third-order iterative schemes for systems. Moreover, each iteration consists only in two steps of Newton's method having the same derivative. With these two properties the scheme becomes a real alternative to the classical Newton method. Affine conjugacy class of the method when is applied to a differentiable function is given. Chaotic dynamics have been investigated in several examples. Applying the root-finding method to a family of degree three polynomials, we have find a bifurcation diagram as those that appear in the bifurcation of the logistic map in the interval.     

Pullback attractors for non-autonomous porous elastic system with nonlinear damping and sources terms

In this paper, we study the asymptotic behavior of a non-autonomous porous elastic systems with nonlinear damping and sources terms. By employing nonlinear semigroups and the theory of monotone operators, we establish existence and uniqueness of weak and strong solutions. We also prove the existence of minimal pullback attractors with respect to a universe of tempered sets defined by the sources terms. Finally, we prove the upper-semicontinuity of pullback attractors with respect to non-autonomous perturbations.     

Navier-Stokes方程的脉动速度方程的最优动力系统建模和动力学分析

研究了基于Navier-Stokes方程的脉动速度方程的最优低维动力系统建模理论.最优目标泛函为脉动速度基函数的不可压缩性和正交性.数值计算了充分发展的并排双方柱绕流问题,并基于双尺度全局最优化方法,建立了它的脉动速度的最优动力系统模型.对其相空间轨道、Poincaré截面、分岔特性、功率谱和Lyapunov指数集等动力学特性进行了分析.随着Reynolds数的增加,双方柱绕流的脉动速度方程最优动力系统具有复杂的类倍周期分岔行为.     

Extended Center Manifold, Global Bifurcation and Approximate Solutions of Chen chaotic dynamical system

The study of the chaotic Chen dynamic System (CDS) has been a recent focus in the literature, with numerous works exploring its various chaotic features. However, the majority of these studies have relied primarily on numerical techniques to investigate nonlinear dynamic systems (NLDSs). In this context, our aim is to derive approximate analytical solutions for the CDS by developing an iterative scheme. We have proven the convergence theorem for this scheme, which ensures that our iterative process will converge to the exact solution. Additionally, we introduce a new method for constructing the extended center manifold, a critical component in the analysis of dynamical systems. The characteristics of the global bifurcation of the system components within the parameter space are explored. The error analysis of the iterated solutions demonstrates the efficiency of the present technique. We present both three-dimensional (3D) and two-dimensional (2D) phase portraits of the system. The 3D portrait reveals a feedback loop pattern, while the 2D portrait, which represents the interaction of the system components, exhibits multiple pools and cross pools. Furthermore, we illustrate the global bifurcation by visualizing the components of the CDS against the space parameters. The sensitivity of CDS to innitesimal variations in the initial conditions (ICs) are tested. It is found that even minor changes can lead to signicant alterations in the system.     

Fractal Dimension of Random Attractors for Non-autonomous Fractional Stochastic Reaction-diffusion Equations

This paper dealswith non-autonomous fractional stochastic reaction-diffusion equations driven by multiplicative noise with s ∈ (0,1). We first present some conditions for estimating the boundedness of fractal dimension of a random invariant set. Then we establish the existence and uniqueness of tempered pullback random attractors. Finally, the finiteness of fractal dimension of the random attractors is proved.