Chaos and mixed synchronization of a new fractional-order system with one saddle and two stable node-foci

This paper reports a new fractional-order Lorenz-like system with one saddle and two stable node-foci. First, some sufficient conditions for local stability of equilibria are given. Also, this system has a double-scroll chaotic attractor with effective dimension being less than three. The minimum effective dimension for this system is estimated as 2.967. It should be emphasized that the linear differential equation in fractional-order Lorenz-like system seems to be less "sensitive" to the damping, introduced by a fractional derivative, than two other nonlinear equations. Furthermore, mixed synchronization of this system is analyzed with the help of nonlinear feedback control method. The first two pairs of state variables between the interactive systems are anti-phase synchronous, while the third pair of state variables is complete synchronous. Numerical simulations are performed to verify the theoretical results.