Hybrid modified function projective synchronization of two different dimensional complex nonlinear systems with parameters identification

In this article, a novel synchronization scheme is proposed to achieve hybrid modified function projective synchronization (HMFPS) in two different dimensional complex nonlinear systems with fully unknown parameters. In the complex space, the response system are asymptotically synchronized up to the different order's drive system by the state transformation with a scaling function matrix, and all of unknown parameters in both drive and response systems are achieved to be identified. Based on the Lyapunov stability theory, an adaptive controller and updated laws of parameters are developed. Respectively on the ways of increased order and reduced order, the corresponding numerical simulations demonstrate the effectiveness and feasibility of the proposed scheme.