Reducible Volterra retarded equations with infinite delay (Q2390111)

The authors investigate the global solutions of the Volterra retarded equations with infinite delay \[ \dot x_j(t)=x_j(t)\left[\varepsilon_j+\displaystyle\sum_{k=1}^ma_{jk}x_k(t)+\displaystyle\sum_{k=1}^mp_{jk}\displaystyle\int_{-\infty}^0e^{\theta}x_k(t+\theta)\,d\theta\right],\tag{1} \] where \(\varepsilon_j,\,a_{jk}\) and \(p_{jk}\) are constants and \(x_j=x_j(t)>0\) for \(j,\,k=\overline{1,m}\). Using the associated reduced system of ordinary differential equations and the corresponding Lotka-Volterra system, they present some existence results for the Lyapunov functions and the global attractors of \((1)\).