AIMS Mathematics, 2020, 5(4): 3089-3110. doi: 10.3934/math.2020199

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Novel fixed-time stabilization of quaternion-valued BAMNNs with disturbances and time-varying coefficients

1 School of Mathematics, Southeast University, Nanjing 210096, China
2 Potsdam Institute for Climate Impact Research, Telegraphenberg, Potsdam D-14415, Germany

In this paper, with the quaternion number and time-varying coefficients introduced into traditional BAMNNs, the model of quaternion-valued BAMNNs are formulated. For the first time, fixed-time stabilization of time-varying quaternion-valued BAMNNs is investigated. A novel fixedtime control method is adopted, in which the choice of the Lyapunov function is more general than in most previous results. To cope with the noncommutativity of the quaternion multiplication, two different fixed-time control methods are provided, a decomposition method and a non-decomposition method. Furthermore, to reduce the control strength and improve control efficiency, an adaptive fixed-time control strategy is proposed. Lastly, numerical examples are presented to demonstrate the effectiveness of the theoretical results.
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