Weak, modified and function projective synchronization of chaotic memristive neural networks with time delays

• A state-feedback controller of weak projective synchronization is designed and unknown control gain is determined.
• An adaptive controller is proposed and unknown control parameters are found to achieve adaptive modified and function projective synchronization..
• In the proof of all theorems, the assumption used in the existing literature is abandoned, and the state switching jumps are concluded in all theorems.

This paper deals with the weak, modified and function projective synchronization issues for chaotic memristive neural networks with time delays. By applying the generalized Halanay inequality, a state-feedback controller is designed, and a novel condition is proposed to ensure the network be weak synchronization with certain error level. By means of Lyapunov–Krasovskii functional approach, the adaptive state-feedback controllers are designed and unknown control parameters are determined by adaptive updated laws to achieve function and modified projective synchronization. Several weak, modified and function projective synchronization conditions are addressed to ensure the synchronization goal. Finally, an illustrative example is given to demonstrate the effectiveness of the theoretical results.