ON THE CHARACTERIZATION OF NONLINEAR OSCILLATOR-SYSTEMS IN CHAOTIC MODE

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 degree of 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.