The criteria of ultimate boundedness for nonautonomous diffusive Lotka-Volterra systems in two heterogeneous patches (Q5943680)

The authors consider the diffusive Lotka-Volterra system (1) in two heterogeneous patches \[ \begin{aligned} \dot{x_i}&=x_i [e_x(t)-A_x(t)x]_i+D_i(t)(y_i-x_i), \quad i\in N,\\ \dot{y_i}&=y_i [e_y(t)-A_y(t)y]_i+D_i(t)(x_i-y_i), \quad i\in N, \end{aligned} \tag{1} \] with \(N=\{1, \ldots, n\}\) and the submodels being Lotka-Volterra tree systems, including Lotka-Volterra chain systems and Lotka-Volterra models between one and multispecies. They obtain a set of sufficient conditions, which is in the explicit form of the parameters and therefore is easily verifiable for the ultimate boundedness of (1).