Initial value problems for ODEs are often solved numerically using adap-tive timestepping algorithms. We formulate a large class of such algorithms as discrete dynamical systems which are discontinuous and of higher dimension than the underlying ODE. By assuming suuciently strong nite-time convergence results on some neighbourhood of an attractor of the ODE we prove existence and upper semicont...

In this paper, relations between the asymptotic behavior for a stochastic wave equation and a heat equation are considered. By introducing almost surely D–α-contracting property for random dynamical systems, we obtain a global random attractor of the stochastic wave equation νutt + ut − uν + f (uν) = √ νẆ endowed with Dirichlet boundary condition for any 0 < ν 1. The upper semicontinuity of thi...

Linear stationary dynamical systems with multiple constant delays in the state are studied. Their relative and approximate controllability properties with constrained controls are discussed. Definitions of various types of controllability with constrained controls for systems with delays in the state are introduced. Some theorems concerning the relative and the approximate relative controllabil...

Introduction: In this paper, a novel complexity measure is proposed to detect dynamical changes in nonlinear systems using ordinal pattern analysis of time series data taken from the system. Epilepsy is considered as a dynamical change in nonlinear and complex brain system. The ability of the proposed measure for characterizing the normal and epileptic EEG signals when the signal is short or is...

The method of triangular functions (TF) could be a generalization form of the functions of block-pulse (Bp)‎. ‎The solution of second kind integral equations by using the concept of TF would lead to a nonlinear equations system‎. ‎In this article‎, ‎the obtained nonlinear system has been solved as a dynamical system‎. ‎The solution of the obtained nonlinear system by the dynamical system throug...

We give an example of a dynamical system which is mixing relative to one of its factors, but for which relative mixing of order three does not hold. 1. Factors, extensions and relative mixing 1.1. Factors, extensions and Rokhlin cocycle. We are interested in dynamical systems (X,A , μ, T ), where T is an ergodic automorphism of the Lebesgue space (X,A , μ). We will often designate such a system...

at the beginning of this paper, design and manufacturing stages of the 3 degree of freedom test stand for a remotely piloted helicopter is described, in which the helicopter is able to rotate about its three primary accesses. in the next parts the dynamical model of the rph in the yaw channel is presented and lateral transfer function of rph (yaw channel) is extracted by performing several test...

We study a reaching movement controller for a redundant serial arm manipulator, based on two principles believed to be central to biological motion control: multireferential control and dynamical system control. The resulting controller is based on two concurrent dynamical systems acting on different, yet redundant variables. The first dynamical system acts on the end-effector location variable...