Multistability and multiperiodicity in impulsive hybrid quaternion-valued neural networks with mixed delays.

The existence of multiple exponentially stable equilibrium states and periodic solutions is investigated for Hopfield-type quaternion-valued neural networks (QVNNs) with impulsive effects and both time-dependent and distributed delays. Employing Brouwer's and Leray-Schauder's fixed point theorems, suitable Lyapunov functionals and impulsive control theory, sufficient conditions are given for the existence of 16 attractors, showing a substantial improvement in storage capacity, compared to real-valued or complex-valued neural networks. The obtained criteria are formulated in terms of many adjustable parameters and are easily verifiable, providing flexibility for the analysis and design of impulsive delayed QVNNs. Numerical examples are also given with the aim of illustrating the theoretical results.