Periodic-Doubling Bifurcation of a Circuit With a Fractional-Order Memristor

A new fractional-order current-controlled memristor is proposed by the fact of the memory loss. Excited by sinusoidal current, the generalized hysteresis loops of the new fractional-order memristor are no longer symmetrical to the origin and the time to reach the steady state is longer than the integer-order memristor’s. The dynamical behaviors of a new fractional-order memristive circuit system whose state variables have different derivation orders are investigated by theoretical analyses and simulated numerically. It is shown that the new fractional-order memristive circuit system goes into chaos by period-doubling bifurcation; the periodic windows are induced by the discontinuous change of derivative order between variables.