Synchronization Analysis of Fractional Order Delayed BAM Neural Networks via Multi-Delay-Boundary Inequality

Abstract

This paper analyzes the synchronization of Caputo fractional-order BAM neural networks with multiple time-varying delays (FOBAMNNs-MTDs). The time-delay phenomenon is inevitable in the synchronization process. Thereby, it is crucial to fully consider the time-delay information on behalf of better studying the synchronization problem. In previously published studies of Caputo FOBAMNNs-MTDs, the time-delay information of bounded MTDs is implied in the delayed state term. Then, the boundary information of MTDs is not considered by applying the method mentioned above, which will be detrimental to the accuracy of the system dynamic characteristics analysis. This paper aims to propose a new time-delay information processing method to enhance the utilization of MTD information, thereby improving the synchronization analysis of FOBAMNNs-MTDs. Firstly, an inequality called multi-delay-boundary inequality (MDBI) containing all boundary information of time-varying delays and fractional-order information is proposed. That is, a new time-delay information processing method of MTDs with different boundary information is proposed, which makes full use of MTD information. Secondly, a less-conservatism synchronization criterion with the information of all delay boundary and fractional-order of Caputo FOBAMNNs-MTDs is established, which is more flexible than the delay-independent criterion. Finally, two numerical simulations are provided to verify the validity of the obtained results.