CHAOTIC BEHAVIOR IN A FRACTIONAL-ORDER SYSTEM CONTAINING A CONTINUOUS ORDER-DISTRIBUTION

This paper discusses the fractional dynamics, and the bifurcation behavior, of a specific nonlinear system that contains a continuous order-distribution. The dynamics of the system are predicted using the describing-function method. General approximation methods are then derived for the continuous order-distribution component. The system is simulated using these approximations, and the results compared with the describing-function predictions. This is believed to be the first observation of chaos in a system with continuous order-distribution.