Existence and attractivity of \(k\)-pseudo almost automorphic sequence solution of a model of bidirectional neural networks (Q1926073)

The author considers the following differential system, which models a neural network: \[ dx_i(t)/dt=-a_i(t)x_i(t)+\sum_{j=1}^m b_{ij}(t)f_j(y_j([t/k]k-[\sigma_{ij}/k]k))+I_i(t), \] \[ dy_i(t)/dt=-c_i(t)y_i(t)+\sum_{j=1}^m d_{ij}(t)g_j(x_j([t/k]k-[\tau_{ij}/k]k))+J_i(t), \] \(i=1,\dots,m\), \([\cdot]\) being the greatest integer function, where \(x_i,y_i\) denote membrane potentials of the \(i\)-th neurons, \(\sigma_{ij},\tau_{ij}\) are time delays, \(I_i,J_i\) are components of an external input source. Along with this system, its discrete analogue is considered. For this discrete system, the author shows the existence and global attractivity of pseudo almost automorphic solutions. An example illustrating applicability of the results is given. The results from \textit{Z. Huang}, \textit{X. Wang} and \textit{Y. Xia} [``Exponential attractor of \(k\)-almost periodic sequence solution of discrete time bidirectional neural networks'', Simul. Model. Pract. Theory 18, 317--337 (2010)] are extended to a more general class of sequences.