Global asymptotic stability of periodic solutions for inertial delayed BAM neural networks via novel computing method of degree and inequality techniques

New results on impulsive type inertial bidirectional associative memory neural networks

“…3. We take into account impulsive effects, so our results are more general than the results in Miao (2013b, 2017), Xu and Zhang (2015), Liao et al (2017), andLi YK andXiang (2019).…”

“…In our model we use variable coefficients for the strong points of the connection and external inputs, because our model is more general than the models in Zhang and Quan (2015) and Aouiti (2018). Liao et al (2017) investigated the same model as in Zhang and Quan (2015) with a variable coefficient. By combining Mawhin's continuation theorem of coincidence degree theory with the Lyapunov functional method and using inequality techniques, the existence and global exponential stability of periodic solutions for NNs were established.…”

“…Using the Lyapunov method and inequality techniques, they showed the uniqueness, existence, and exponential stability of anti-periodic solutions of IBAMNNs. Ke and Miao (2017) discussed the exponential stability of antiperiodic solutions for inertial NNs with time delays, presented hypotheses that help show the existence and exponential stability of anti-periodic solutions for this type of NN, and used the Lyapunov method, uniform convergence, and so on (Ke and Miao, 2011, 2013aHe et al, 2012;Qi et al, 2015;Xu and Zhang, 2015;Zhang and Quan, 2015;Tu et al, 2016;Liao et al, 2017;Li YK and Xiang, 2019).…”

Periodic solutions for complex-valued neural networks of neutral type by combining graph theory with coincidence degree theory

“…In recent years, combination of graph theory with coincidence degree theory has been applied to studying the existence of periodic solutions for coupled networks [31][32][33][34][35]. Recently, we have established some sufficient conditions for the existence and global stability of periodic solutions for neural networks by combining coincidence degree theory with Lyapunov functional method [14,15,37]. However, the results on the existence and global stability of periodic solutions for neural networks have not been obtained by combining coincidence degree theory with graph theory as well as Lyapunov functional method.…”

“…Recently, without applying the a priori estimate method of periodic solutions, we have established some criteria to guarantee the existence of periodic solutions for neural networks with time delays by combining coincidence degree theory with Lyapunov functional method or linear matrix inequality method [14,15,37].…”