Abstract
In this paper, chaotic behavior in a piecewise continuous map(PCM) associated with sine circle maps of nonlinear systems of Van der Pol-Mathieu type is studied. At first, a sine circle map and its approximate PCM are derived. Secondly, based on computational experiments on Lyapunov exponents to approximate PCM, existence conditions are shown to generate chaotic oscillation and periodic oscillation in PCM. Finally, it is shown that the rotation numbers of oscillation in PCM form a part of successive Farey series and form devil's stairs in the region of cut off parameter such that Lyapunov exponent is positive. Furthermore, it is shown that the order of appearance of the oscillation in PCM has a self similar hierarchy.
