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Abstract
Some dynamical behaviors of fractional-order commutative quaternion-valued neural networks (FCQVNNs) are studied in this paper. First, because the commutative quaternion does not satisfy Schwartz triangle inequality, the FCQVNNs are divided into four real-valued neural networks (RVNNs) through quaternion commutative multiplication rules. Furthermore, several types of dynamical behaviors including global Mittag-Leffler stability, the boundedness with bounded disturbances, complete synchronization and quasi-synchronization of FCQVNNs are studied. Simultaneously, several conditions for these dynamical behaviors are driven by fractional-order Lyapunov direct method, some inequality techniques and fractional differential equation theory. At last, the effectiveness and feasibility of the obtained theoretical results are verified by several numerical simulation examples.
Highlights
Fractional calculus and fractional-order neural networks (FNNs) have become hot research topics
We prove the uniqueness and existence of the equilibrium point for the fractional-order commutative quaternion-valued neural networks (FCQVNNs) after transformation, and discuss the dynamic conclusions of the global Mittag-Leffler stability and boundedness
According to the above methods, this paper will be extended to a certain extent, so that it can be used to a greater extent to analyze and solve the dynamics problems of FCQVNNs
Summary
Fractional calculus and fractional-order neural networks (FNNs) have become hot research topics. In the related research of the existing fractional commutative quaternion-valued neural networks (FCQVNNs), the theoretical tools used in different studies in the literature are not the same, and there is no unified and effective analysis method. In order to analyze these systems more conveniently, the FCQVNNs will be divided into real-valued systems, based on fractional-order Lyapunov direct method, some conditions of stability and boundness are proposed. Using this approach, we prove the uniqueness and existence of the equilibrium point for the FCQVNNs after transformation, and discuss the dynamic conclusions of the global Mittag-Leffler stability and boundedness. The effectiveness and feasibility of these conclusions will be demonstrated by MATLAB numerical simulation experiments
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