Global matrix projective synchronization of delayed fractional-order neural networks

This paper extends the projection scaling factor to a general constant matrix and research the global matrix projection synchronization (GMPS) for the delayed fractional-order neural networks (DFONNs) by using the sliding mode controller (SMC). GMPS is far more complex and difficult than other general synchronization types, so it can enhance the strong confidentiality and high security. Firstly, for the DFONNs, the optimal sliding surface and SMC are constructed. Secondly, the sufficient condition for achieving GMPS is presented. Moreover, the error system’s reachability and stability are analyzed and proved, and the GMPS is realized well. At last, the trajectories of error system and GMPS of state variables for a three-dimensional example are simulated to verify the feasibility of synchronization theory analysis. Particularly, GMPS can be reduced to the complete synchronization, anti-synchronization, projective synchronization (PS) and modified PS. This research will expand the synchronization theory of fractional-order neural networks (FONNs) and gives a general method to realize the GMPS of other fractional-order systems.