Dual Event-Triggered Synchronization of Two-Time-Scale Jumping Neural Networks and Its Application in Image Encryption and Decryption

Synchronization of neural networks has found widespread applications in practice. The existing results about the event-triggered synchronization of two-time-scale neural networks/systems mainly design a <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">common</i> event-triggered mechanism using <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">single</i>-rate sampling method on different time scales, which ignores the two-time-scale characteristics and may lead to a suboptimal reduction in communication burden on different time scales. This paper concentrates on <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">dual</i> event-triggered synchronization issues for two-time-scale jumping neural networks. The neural networks are modeled with two-time-scale structures and the changes of jumping parameters follow the Markov process. First, a <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">double</i>-rate sampling method is adopted and the dual event-triggered mechanism is proposed, which contains two separate event-triggered conditions for different time scales states. Then, sufficient conditions are established for the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$H_{\infty }$</tex-math></inline-formula> performance analysis of the two-time-scale jumping neural networks while considering the dual event-triggered mechanism. Moreover, based on the above conditions, the controller gains are derived to achieve the event-triggered synchronization of the neural networks. At last, the availability of the proposed approach is demonstrated via two examples, in which image encryption and decryption are used to illustrate the application prospects of the synchronization for two-time-scale jumping neural networks.