Simulation of two-species population growth for the model (1) and model (2).

In the case of model (1) type X and Y cross-feed each other and in the case of model (2) X_c doesn't cross-feed Y but Y cross-feeds X_c. Here we plot X(t) solution of (1) (full line) together with X_c(t) solution of (2) (dashed line) with A. r_y = 0.011, r_x = 0.008,  = 0.009, b_xy = b_yx = 0.01; B. r_y = 0.011, r_x = 0.008,  = 0.009, b_xy = b_yx = 0.001; C. r_y = 0.03, r_x = 0.015,  = 0.025, b_xy = b_yx = 0.01. For both simulations of model (1) and (2) and in all three cases presented here K = 10000, and ε₁ = ε₂ = 0.01.