Projective synchronization results of fractional order quaternion valued neural networks with proportional delay under event-triggered control

Abstract

This paper explores the projective synchronization (PS) of fractional order neural networks (FONNs) with proportional delay in quaternion through non-decomposition method. A controller with proportional delay is designed from the perspective of reducing the times of controller updates and computational costs, and corresponding event-triggered conditions are provided. The criteria for achieving PS of the systems are obtained through techniques such as mean value inequality and Razumikhin’s theorem. On the basis of this derivation, the conditions for systems to achieve PS are explored when two consecutive releases are fixed. In addition, the positive lower bound of the inter-event time is derived, Zeno behavior can be excluded. Finally, the validity of the theoretical results is obtained through simulation. Additionally, the application of the system studied in this paper in image encryption and decryption is presented.