Global existence of bifurcating solutions to a two-box prey-predator model (Q1321769)

The author considers a two-box prey-predator model described by \[ {ds_1 \over dt} = d_s (s_2 - s_1) + f(s_1, x_1),\;{dx_1 \over dt} = d_x (s_2 - s_1) + g(s_1, x_1), \] \[ {ds_2 \over dt} = d_s (s_1 - s_2) + f(s_2, x_2),\;{dx_2 \over dt} = d_x (s_1 - s_2) + g(s_2, x_2), \] where \(s_i\) and \(x_i\) are respectively the population of the prey and of the predator in the box \(i\) \((i = 1,2)\), \(d_s\) and \(d_x\) respectively the magnitude of diffusion of the prey and the predator. The terms \(d_s (s_1 - s_2)\), \(d_x (s_1 - s_2)\), \(d_s (s_2 - s_1)\), \(d_x (s_2 - s_1)\) represent the migration effect between the two boxes. The author obtains a complete global bifurcation diagram of all the nonnegative equilibria of the system as well as additional results on global existence and stability of the bifurcating solutions.