Global asymptotic stability of high-order delay Hopfield neural networks with time-varying coefficients
Using the Brouwer fixed-point theorem and the method of Lyapunov functionals, the authors find conditions for existence and global asymptotic stability of the equilibrium of neural networks of the type \[ u_i'(t)= -a_i(t) u_i(t)+ b_i(t)+ \sum_j W_{ij}(t) g_j(u_j(t- \tau))+ \sum_{j,k} W_{ijk}(t) g_j(u_j(t-\tau)) g_k(u_k(t- \tau)), \] \(i= 1,2,\dots, n\). Here, \(a_i\), \(b_i\), \(g_i\), \(W_{ij}\) and \(W_{ijk}\) are continuous bounded functions and \(a_i(t)> 0\).
scientific article; zbMATH DE number 5011364