Global Dissipativity Analysis and Stability Analysis for Fractional-Order Quaternion-Valued Neural Networks With Time Delays

This article studies dissipativity analysis of fractional-order quaternion-valued neural networks (FOQVNNs) with time delays. Two specific activation functions are considered along with common bounded and activation functions of Lipschitz-kind. Since quaternion multiplication is not commutative, we must divide the model, which is evaluated by quaternion, into four elements that are real-valued elements. On the basis of the construction of novel Lyapunov functional, and applying fractional-calculus theory, new criteria for the test of the global dissipativity and exponential stability of FOQVNNs model are established. FOQVNNs have also been suggested to provide global dissipativity and exponential stability, whereas nonlinear complex activation functions are constrained by the usage of linear matrix inequality methods, which utilize quaternion matrices and positive quaternion definite matrices. Finally, the effectiveness and superiority of the proposed approach is validated through numerical examples.