# Existence, uniqueness, and global asymptotic stability analysis for delayed complex-valued Cohen–Grossberg BAM neural networks

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## Abstract

This paper investigates the existence, uniqueness, and global asymptotic stability of equilibrium point for a complex-valued Cohen–Grossberg delayed bidirectional associative memory neural networks. The two types of complex-valued behaved functions, amplification functions and activation functions, are considered. By using homeomorphism theory and inequality technique, the sufficient conditions for the existence of unique equilibrium point are obtained. Then, by constructing a suitable Lyapunov–Krasovskii functional, the global asymptotic stability condition of the proposed neural networks is derived in terms of linear matrix inequalities. This linear matrix inequality can be efficiently solved via the standard numerical packages. Finally, the numerical examples are given to validate the effectiveness of theoretical results.

## Keywords

Complex-valued Cohen–Grossberg BAM neural networks Existence and uniqueness of equilibrium point Global asymptotic stability Linear matrix inequalities Time delays## Notes

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### Conflict of interest

The authors declare that there is no conflict of interests regarding the publication of this paper.

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