Uniform approximation of impulsive Hopfield cellular neural networks by piecewise constant arguments on \([\tau,\infty)\)
The paper deals with an approximation on a semi-axes \([t_0,\infty)\) the following non-linear impulsive system \[ y'_i(t)=-a_i(t)y_i(t)+\sum_{j=1}^m b_{ij}(t)f_j(y_j(t))+c_i(t),~~t\neq t_k, \]\[ \Delta y_i(t_k)=-q_{i,k}y_i(t_k^-)+e_{i,k}+I_{i,k}(y_i(t_k^-)),~~t=t_k, ~ y_i(t_0)=y_i^0 \] by the system \[ z'_i(t)=-a_i(t)z_i(t)+\sum_{j=1}^m b_{ij}(t)f_j(z_j(\gamma(t)))+c_i(t),~~t\neq \gamma (t_k), \]\[ \Delta z_i(\gamma (t_k))=-q_{i,k}z_i(\gamma (t_k)^-)+e_{i,k}+I_{i,k}(z_i(\gamma (t_k)^-)),~~t=\gamma (t_k), ~ z_i(t_0)=z_i^0, \] where \(\gamma(t)\) a piecewise constant argument.
scientific article; zbMATH DE number 7349874
scientific article