Existence and stability of periodic solution for BAM neural networks with distributed delays

摘要

We use the continuation theorem of coincidence degree theory and Liapunov functions to study the existence and stability of positive periodic solutions for a class of two-layer heteroassociative networks called bidirectional associative memory networksdxidt=−ai(t)xi(t)+∑j=1mpji(t)fj(yj(t−τji(t,yj(t))))+Ii(t),i=1,2,…,n,dyjdt=−bj(t)yj(t)+∑i=1nqij(t)fi(xi(t−σij(t,xi(t))))+Jj(t),j=1,2,…,manddxidt=−ai(t)xi(t)+∑j=1mpji(t)fj∫0∞hji(s)yj(t−s)ds+Ii(t),i=1,2,…,n,dyjdt=−bj(t)yj(t)+∑i=1nqij(t)fi∫0∞kij(s)xi(t−s)ds+Jj(t),j=1,2,…,m.