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Stability analysis of quaternion‐valued Cohen‐Grossberg neural networks
Author(s) -
Li Ruoxia,
Gao Xingbao,
Cao Jinde,
Zhang Kai
Publication year - 2019
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.5607
Subject(s) - quaternion , exponential stability , mathematics , equilibrium point , artificial neural network , stability (learning theory) , quaternion algebra , algebra over a field , point (geometry) , control theory (sociology) , pure mathematics , artificial intelligence , mathematical analysis , computer science , division algebra , differential equation , machine learning , geometry , algebra representation , nonlinear system , physics , control (management) , quantum mechanics
In this paper, by starting from basic quaternion algebra properties and algorithms, a quaternion‐valued Cohen‐Grossberg neural network was derived, subsequently, several new sufficient conditions are derived to ensure existence and global asymptotic stability (GAS) and global exponential stability (GES) of the equilibrium point (EP) for quaternion‐valued Cohen‐Grossberg neural networks. The obtained criteria can be checked easily in practice and have a distinguished feature from previous studies. Finally, we have numerical evidences that the mathematical system and the conclusions presented are validated.