Copyright © 2013 Mervan Pašić and Satoshi Tanaka. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We derive some simple sufficient conditions on the amplitude , the phase and the instantaneous frequency such that the so-called chirp function is fractal oscillatory near a point , where and is a periodic function on . It means that oscillates near , and its graph is a fractal curve in such that its box-counting dimension equals a prescribed real number and the -dimensional upper and lower Minkowski contents of are strictly positive and finite. It numerically determines the order of concentration of oscillations of near . Next, we give some applications of the main results to the fractal oscillations of solutions of linear differential equations which are generated by the chirp functions taken as the fundamental system of all solutions.