Existence and exponential stability of almost periodic solution for Hopfield-type neural networks with impulse (Q937322)

In \(\mathbb{R}^n\) the authors consider an impulsive differential equation of the form \[ {dx\over dt}=- a_i(t) x_i(t)+ \sum^n_{j=1} p_{ij}(t) f_j(x_j(t))+ c_i(t),\quad t\neq t_k,\;i= 1,2,\dots,n, \] \[ \Delta x_i(t_k)= x_i(t^+_k)- x_i(t^-_k) \] and find sufficient conditions for the existence of a unique almost periodic solution. Under additional conditions the solution is exponentially stable.