Finite-time and fixed-time function projective synchronization of competitive neural networks with noise perturbation

In this paper, finite-time and fixed-time function projective synchronization of competitive neural networks with time-varying delays and noise perturbation is studied. Firstly, different from the existing papers, a more flexible Lyapunov function is constructed based on p-norm and two hybrid controllers are designed in this paper. Secondly, based on the finite-time and fixed-time stability theory and stochastic analysis theory, some new and useful finite-time and fixed-time function projective synchronization criteria are obtained. Furthermore, the settling time is derived with the help of some lemmas and mathematical inequalities under the appropriate control scheme. Finally, illustrative examples are given to show the feasibility of the proposed method.