This study is to analyse the dynamical instability (or the buckling) of a steel space truss using the accurate solutions obtained by the high-order Taylor series method. One is used to obtain numerical solutions for analysing instability, because it is difficult to find the analytic solution for a geometrical nonlinearity system. However, numerical solutions can yield incorrect analyses in the ...

In many situations it is desirable to compare dynamical systems based on their behavior. Similarity of behavior often implies similarity of internal mechanisms or dependency on common extrinsic factors. While there are widely used methods for comparing univariate time series, most dynamical systems are characterized by multivariate time series. Yet, comparison of multivariate time series has be...

‎In this paper we investigate the dilations of completely positive definite representations‎ ‎of (C^ast)-dynamical systems with abelian groups on Hilbert (C^ast)-modules‎. ‎We show that if ((mathcal{A}‎, ‎G,alpha)) is a (C^ast)-dynamical system with (G) an abelian group‎, ‎then every completely positive definite covariant representation ((pi,varphi,E)) of ((mathcal{A}‎, ‎G,alpha)) on a Hilbert ...

a semi-batch crystallization system is used to determine growth kinetics and morphology of barium carbonate crystals, under a constant ph value and constant temperature in the various relative supersaturations. results show that crystal growth rate satisfies a first-order kinetic expression at high relative supersaturation, while at relative supersaturation values lower than 3,  the kinetic exp...

Preface In the beginning of 90s the authors of this monograph proposed a generalization of the concept of hyperbolicity, first for differentiable mappings and later for Lipschitz mappings, which they called 'semi-hyperbolicity'. This arose indirectly in the context of their research at that time on the effect of spatial discretization on the behavior of a dynamical system, in particular that of...

The relationship between random attractors and global attractors for dynamical systems is studied. If a partial differential equation is perturbed by an −small random term and certain hypotheses are satisfied, the upper semicontinuity of the random attractors is obtained as goes to zero. The results are applied to the Navier-Stokes equations and a problem of reaction-diffusion type, both pertur...

We continue the study of Rokhlin entropy, an isomorphism invariant for p.m.p. actions of countable groups introduced in Part I. In this paper we prove a non-ergodic finite generator theorem and use it to establish subadditivity and semi-continuity properties of Rokhlin entropy. We also obtain formulas for Rokhlin entropy in terms of ergodic decompositions and inverse limits. Finally, we clarify...

Invariance properties and convergence of solutions of set dynamical systems are studied. Using a framework for systems with set-valued states, notions of stability and detectability, similar to the existing results for classical dynamical systems, are defined and used to obtain information about the convergence properties of solutions. In particular, it is shown that local stability, detectabil...

When studying a metastable dynamical system, a prime concern is how to decompose the phase space into a set of metastable states. Unfortunately, the metastable state decomposition based on simulation or experimental data is still a challenge. The most popular and simplest approach is geometric clustering which is developed based on the classical clustering technique. However, the prerequisites ...