Stability loss delay in harvesting competing populations
Consider the differential system \[ dx/dt = xM(x,y,E), \;dy/dt=y N(x,y), \;dE/dt = \varepsilon E P(x),\tag{*} \] describing the dynamics of two competing populations \(x\) and \(y\) under a harvesting effort \(E\) with a slow growth rate \((\varepsilon\) is small). \(M\) and \(N\) are such that, in case of no harvesting, one of the species disappears. The author proves that the harvesting effort leads to the existence of a relaxation oscillation (no extinction). It is shown that the oscillation is of canard type (the phenomenon of delayed loss of stability occurs).
scientific article; zbMATH DE number 1283669