Adaptive synchronization of neural networks with different attractors (Q2644708)

The subject of the paper are neural networks of the type \[ \dot x_i = -a_i x_i(t) + \sum_{i=1}^{n} b_{ij} g_j(x_j(t))+ \sum_{j=1}^{n} c_{ij} g_j(x_j(t-\tau_j(t)))+U_i,\quad i=1,\dots,n, \tag{1} \] where \(U_i=\text{const}\), \(a_i>0\), \(\dot \tau_i (t)\leq \mu<1\). Assuming that (1) drives another network, the following control problem is considered \[ \dot y_i = -d_i y_i(t) + \sum_{i=1}^{n} e_{ij} f_j(y_j(t))+ \sum_{j=1}^{n} m_{ij} f_j(y_j(t-h_j(t)))+H_i+u_i(t,x,y), \] where \(u_i(t,x,y)\) is the control input, which should be designed to obtain complete synchronization of drive and response system, i.e. \(\lim_{t\to\infty}| x_i-y_i| =0\) for all \(n\). The control \(u(t,x,y)\) and sufficient conditions for synchronization are given.