Time Evolution Of Nonlinear Systems Research Articles

Experimental Detection of Nonlinear Dynamics Using a Laser Profilometer

This paper investigates a cantilever beam nonlinear dynamic behaviour, on which the nonlinearity is introduced with permanent magnet interactions or with a non-holonomic contact. The experimental time domain responses obtained from non-zero initial conditions are measured using a laser profilometer, conventionally adopted for product shape detections in online industrial applications. The Fourier transform, Continuous Wavelet transform, and Hilbert transform are used to investigate nonlinear phenomena in the frequency content, highlighting advantages and drawbacks of the three methods in catching instantaneous phenomena. Then, a Multi-Phi approach is proposed to describe the time evolution of nonlinear systems by means of a discrete number of linearised systems. Therefore, two linearised models have been developed and tuned to describe the dynamic behaviour of different Euler–Bernoulli cantilever beam configurations. The experimental data of nonlinear systems are compared with the corresponding ones of the linear system to evaluate the effects of introduced nonlinearities on the overall dynamic properties.

Using artificial neural networks to forecast chaotic time series

Two-layer feedforward neural network was used in this work to forecast chaotic time series with very promising results, especially for the Lorenz system, as in comparison to others that had been previously published elsewhere. It was observed that the architecture m:2m:m:1, where m is the embedding dimension of the attractor of the dynamical system in consideration, is a very good initial guess for the process of finding the ideal architecture for the neural network, which is usually hard to achieve. The results we obtained with this particular type to series, and also with some others like Henon and Logistic maps, clearly indicate that there is an interplay between the architecture of a multilayer network and the embedding dimension m of the time series used. From the very good forecasting results we obtained, it can be concluded that neural networks can be considered to be an important tool for making predictions of the time evolution of nonlinear systems.

The nonlinear paradigm: Advancing paradigmatic progress in the policy sciences

AbstractThis paper responds to Daneke 's call for a new systems paradigm in the policy sciences. The nonlinear paradigm is presented as one perspective that may add to this new paradigm. The nonlinear paradigm explores the complex, uncertain, and sometimes unstable time evolution of nonlinear systems. The paper identifies and examines elements of the nonlinear paradigm that have particular relevance for understanding and contending with policy problems. The lessons learned and the tools utilized by this emerging perspective are presented as a means for furthering paradigmatic progress in the policy sciences.