Jump resonance in fractional order circuits

In this communication, the first example of fractional order nonlinear system showing jump resonance is described, that is a system in which the order of the derivative is non-integer and whose frequency response is a multi-valued function in a given range of frequencies. Furthermore, a strategy to design fractional order systems showing jump resonance is presented along with the procedure to design and implement an analog circuit based on the approximation of the fractional order derivative. An extensive numerical analysis allows to asses that the phenomenon is robust to difference in the derivative order, enlightening the fact that a system with order lower than two is able to provide a jump resonance behavior.