Finite-time quasi-projective synchronization of fractional-order reaction-diffusion delayed neural networks

This paper investigates the finite-time quasi-projective synchronization (FTQPS) issue of fractional-order reaction-diffusion neural networks (FORDNNs). To the best of our knowledge, this paper introduces the concept of FTQPS for the first time. First, an integral-type Lyapunov function is constructed relying on the characterization of the reaction-diffusion term and some inequality methods. Subsequently, the nonlinear feedback control strategy is designed to achieve the FTQPS goal and some sufficient conditions are obtained to guarantee FTQPS of FORDNNs. Further, the system's synchronization speed is measured by estimating the settling time. It should be noted that the above control strategy is also applicable to conventional integer-order reaction-diffusion neural networks with time delays. Finally, a numerical example is used to illustrate the validity of the theoretical analysis presented.