Anti-synchronization of inertial neural networks with quaternion-valued and unbounded delays: Non-reduction and non-separation approach

This article investigates the anti-synchronization (AS) problem for quaternion-valued inertial neural networks (QVINNs) with unbounded time delays. Using two different types of control strategies (feedback and adaptive controllers) and Lyapunov theory, various conditions are established to guarantee the AS of QVINNs. Most of the results available for QVINNs are based on the variable substitution approach, which reduces the order of the original second-order system into the first-order system. The quaternion-valued networks can be separated into four equivalent real-valued neural networks (RVNNs), which have made the process more complicated. However, in the present study, the authors deal with the non-reduction order method and non-separation approach for QVINNs, making the analysis approach more concise and easier to deal with inertial neural networks (INNs). Here, the QVINNs have unbounded time-varying delays since neurons’ actions are related to their previous states. Hence the approach adopted here is more realistic and easy to deal with the QVINNs with unbounded time delays, which has not yet been considered by any researcher. Finally, two numerical examples are provided to demonstrate the efficiency and effectiveness of the proposed approach. In the first example, the present theoretical results have been validated, whereas the second example contains the application of quaternion-valued neural networks (QVNNs) related to associative memory to demonstrate their capacity to restore true color image patterns accurately. •Global anti-synchronization for a class of quaternion-valued inertial neural with unbounded time delays is done.•Quaternion feedback and adaptive control schemes are used for the antisynchronization results.•Non-reduction order and non-separation approaches for second-order quaternion systems are used.•Lyapunov functional is used for the control scheme.•In this work, the discrete time-varying delays are unbounded.•Showcasing of validation of theoretical results through a numerical example.•The numerical simulation demonstrates that the quaternion-valued neural networks are effective in storing and retrieving true-color images.