Global asymptotic stability of periodic solutions for delayed complex-valued Cohen-Grossb erg neural networks by combining coincidence degree theory with LMI method

The paper is concerned with the existence and global asymptotic stability of periodic solutions for a class of delayed complex-valued Cohen-Grossberg neural networks. Without using the method of the a priori estimate of periodic solutions, by combining Mawhin's continuation theorem of coincidence degree theory with LMI method and using inequality techniques, a novel LMI-based sufficient condition on the existence of periodic solutions is established for the complex-valued Cohen-Grossberg neural networks. Then by using inequality techniques, a novel sufficient condition on the global asymptotic stability of periodic solutions for the above complex-valued neural networks is established. Our results and method are new and complementary to the existing papers on the study of periodic solutions of neural networks. (C) 2018 Elsevier B.V. All rights reserved.