Analysis of a Fractional Order Nonlinear System Based on the Frequency Domain Approximation

Abstract

The dynamics of nonlinear system is very complicated especially the fractional nonlinear system since they can be found in many areas of engineering and science. The dynamics of the Lorenz system with fractional derivatives is analysed based on the frequency approximation. For a given range of parameters where the non-fractional Lorenz system has periodic orbits, it is found that the fractional Lorenz system exhibits chaos and hyperchaos. A striking finding is that the fractional Lorenz system exhibits hyperchaos, although the total system order is less than 3, which is contrary to the well known conclusion that hyperchaos cannot occur in the integer-order continuous-time autonomous system of order less than 4. Finally, a reasonable explanation is offered for this complicated dynamical phenomenon.