Stability analysis and synchronization application for a 4D fractional-order system with infinite equilibria

This paper reports a 4D fractional-order memristor-based system with the flux-controlled memristor characterized by a cubic smooth monotonically increasing function. An unusual phenomenon is the fractional-order system has infinite equilibria. It is found that the local stability of these equilibria could be divided into three categories by the aid of local linearization technique. For those unstable equilibrium points, the dynamical behavior of the 4D fractional-order system depends on the differential order and initial conditions simultaneously. Through building a drive- response configuration, complete synchronization could be achieved with the proper initial value of response system. Finally, a novel information transmission scheme has been designed based on the switch synchronization of the fractional-order system, which has a larger key space. Two different types of information signals are taken as examples to verify the effectiveness of the proposed secure communication scheme.