Figure 2
From: Multi-species coexistence in Lotka-Volterra competitive systems with crowding effects
Modified LV competition system with nonlinear crowding effect using the four possible cases of isoclines for the crowding strength factor δ. All non-coexistence patterns (a,b,d) move to coexistence as δ → 1.0 and return to competitive exclusion as δ → 5.0. The right column figures show the equilibrium points in the x1 − x2 phase plane. (a) \(({K}_{2} < \frac{{K}_{1}}{{\alpha }_{12}},{K}_{1} > \frac{{K}_{2}}{{\alpha }_{21}})\), (b) \(({K}_{2} > \frac{{K}_{1}}{{\alpha }_{12}},{K}_{1} < \frac{{K}_{2}}{{\alpha }_{21}})\), (c) \(({K}_{2} < \frac{{K}_{1}}{{\alpha }_{12}},{K}_{1} < \frac{{K}_{2}}{{\alpha }_{21}})\), and (d) \(({K}_{2} > \frac{{K}_{1}}{{\alpha }_{12}},{K}_{1} > \frac{{K}_{2}}{{\alpha }_{21}})\). Colors indicate x1(red) and x2 (blue). Parameter value and software used: see Fig. 1.
