Partial switched modified function projective synchronization of unknown complex nonlinear systems

Many studies on the switched modified function projective synchronization of nonlinear real dynamic systems have been carried out, whereas the switched modified function projective synchronization of chaotic complex systems has not been studied extensively. In this paper, the concept of the partial switched modified function projective synchronization of complex nonlinear systems with fully unknown parameters is proposed. Partial switched synchronization of chaotic systems means that the state variables of the drive system synchronize with partial different state variables of the response system. Based on the parameter modulation and the adaptive control technique, the adaptive control laws and the parameter update laws are derived to make the states of two different complex nonlinear systems asymptotically synchronized up to a desired scaling function matrix. The given scaling function can be an equilibrium point, a periodic orbit, or even a chaotic attractor in the phase space. Finally, numerical simulations are performed to verify the feasibility and effectiveness of the proposed controllers and identifiers.