Crossings of homoclinic manifolds is a well known mechanism underlying observed chaos in low dimensional systems. We discuss an analogous situation as it pertains to the numerical simulation of a well known integrable partial differential equation, the nonlinear Schrödinger equation. In various...

Various remarkable nonlinear phenomena have been confirmed, discovered and explored through computer simulations of nearly integrable, Hamiltonian, large dimensional lattices with periodic boundary conditions. Here we pick the periodic sine-Gordon example of an “a priori unstable” integrable...

A difference scheme of a system of nonlinear partial differential equations describing 2N-wave interaction (9n = 1,2,....N,Uo=uN+1=0)Δ+xun(x,y)=un(x+δ,y)υn(x,y+ε)−un(x,y)υn+1(x,y),Δ+yun(x,y)=υn(x,y+ϵ)un−1(x+δ,y)−υn(x,y)un(x,y), is obtained preserving an integrability of the system.

Selftuning of classical PI-controllers for processes without known mathematical models is achieved by applying heuristic fuzzy rules. Step changes of the reference input are used to assess control performance in terms of overshoot, rise time and setting time of the step response. Similar to the...

The present state of affairs in the description of real systems with chaotic dynamics calls for a new approach aimed at a more complete description of experiments. Such a description takes into account explicitly the inevitable uncertainties by means of an appropriate mathematical formalism and...

Light propagation in optical waveguides is studied in the paraxial approximation using Richardson extrapolation and the mid-step Euler finite difference algorithm. Highly accurate solutions can be efficiently obtained using this combined approach. Since discretization errors in both the...

The inverse scattering transform (IST) for the periodic Kortweg—de Vries (KdV) equation in the μ-function representation is considered and numerical formulations are given (1) for determining the direct scattering transform spectrum of an input discrete wave train and (2) for reconstructing...

The recursive Newton—Euler formulation to compile or compute the robot dynamics is essential for problems of robot simulation as well as for robot inverse dynamics. Beside the established form of computation in outward (forward) and inward (backward) recursion, several schemes that exploit...

Numerical simulation is used more and more for analyzing physical phenomena. Starting from a mathematical model of the phenomenon, the simulation consists in solving it on a computer, using numerical methods. Unfortunately results provided by the computer always contain errors resulting both...

This paper provides two simple results by which complex systems can be identified as sets of interconnected subsystems and their respective interconnections.