On the characterization of non-linear oscillator systems in chaotic mode

Abstract

The chaotic response of certain non-linear systems is now a well documented fact. Many techniques have been put forward to characterize such responses. These characterization techniques have proved valuable in determining whether or not a system is chaotic; however, the degreeof complexity of a chaotic system is much more difficult to define. With the increase in the use of such techniques to characterize multi-degree-of-freedom systems in experimental practice, there is a need for the results of such characterization techniques to be more than a simple answer to the question, “Is the system chaotic?” but rather, “How chaotic is the system?”. Two systems of non-linear oscillators are presented—one system chaotically excited and the other elastically coupled. Both systems are based on the Duffing oscillator. The chaotic response of these systems is characterized by using the Grassberger-Procaccia dimension algorithm. As the number of oscillators in each system increases, there is a marked change in the complexity of the response of both systems. The overall behaviour of the two systems is explored, and reported upon, herein.