In this study, multimode chaos observed from two coupled chaotic oscillators with hard nonlinearities is investigated. At first, a simple chaotic oscillator with hard nonlinearities is realized. It is confirmed that in this chaotic oscillator the origin is always asymptotically stable and that the solution, which is excited by giving relatively large initial conditions, undergoes period-doublin...

BACKGROUND The six item Confusion, Hubbub and Order Scale (CHAOS-6) has been validated as a reliable tool to measure levels of household disorder. We aimed to investigate the goodness of fit and reliability of a new Malay version of the CHAOS-6. METHODS The original English version of the CHAOS-6 underwent forward-backward translation into the Malay language. The finalised Malay version was a...

Biogeography-based optimization (BBO) has shown excellent exploitation ability of the population information for simple-objective optimization problem. But if BBO is directly applied in multi-objective optimization problems (MOPs), optimal solution set gained by BBO has worse diversity and distribution. To overcome these shortcomings, a chaos migration operator is put forwards to improve the di...

Model reduction attempts to guarantee a desired “model quality”, e.g. given in terms of accuracy requirements, with as small a model size as possible. This article highlights some recent developments concerning this issue for the so called Reduced Basis Method (RBM) for models based on parameter dependent families of PDEs. In this context the key task is to sample the solution manifold at judic...

Most engineers are (indirectly) trained to be “feedforward thinkers” and they immediately think of “model inversion” when it comes to doing control. Thus, they prefer to rely on models instead of data, although feedback solutions in most cases are much simpler and more robust∗.

Much of engineering is concerned with the topic of optimization, and at the heart of much of our optimization is dynamical systems. Dynamical systems can be thought of as either non-linear continuous-time differential equations or difference equations. Chaos occurs in dynamical systems, and frequently in engineering we seek to avoid chaos. At times chaos becomes the central fascination. This pa...