Fig. 1
Experimental (a,c) and Numerical (b,d) Anisotropic Interspecies Competition.
Table 1
Model variables and parameters associated with System (3).
| Variables | Description |
|---|---|
| M, W | The density of species 1 and 2 |
| C | The concentration of the chemical |
| U, P | The velocity and the pressure of the fluid |
| Q, R and S | The anisotropic diffusive tensors |
| a(M), b(W) | The density-dependent diffusion coefficients |
| χ1(M), χ2(W) | The chemotactic sensitivity functions |
| μ1, μ2 > 0 | The growth rate of populations 1 and 2 |
| α1, α2 > 0 | The strength of populations 1 and 2 in competition |
| α, β > 0 | The consumption rate of chemicals by populations 1 and 2 |
| The external gravitational force exerted by the species 1 and 2 on the fluid |
Fig. 2
Primal and dual meshes.
Fig. 3
Coexistence of two species M and W (left), Species 1 win (middle), Species 2 win (right).
Fig. 4
Mesh 1 of 352 diamonds (left), Mesh 2 of 1928 diamonds (middle), Mesh 3 of 5440 diamonds (right).
Fig. 5
Random densities of species 1 (left), Density of species 1 after 20s; 10−23 ≤ M ≤ 10−11 (middle), Extinction of species 1 (right).
Fig. 6
Random densities of species 2 (left), Density of species 2 after 20 s ; 0.994 ≤ W ≤ 0.999 (middle), Evolution in time of winner species 2 density (right).
Table 2
Relative errors-Mesh size =h= 0.54 × 10−2.
| M(t = 1) | W(t = 1) | M(t = 3) | W(t = 3) | M(t = 5) | W(t = 5) | |
|---|---|---|---|---|---|---|
| Relative L2-error | 3.09 × 10−6 | 3.36 × 10−7 | 1.21 × 10−7 | 1.16 × 10−7 | 6.43 × 10−8 | 6.80 × 10−8 |
| Relative L∞-error | 1.76 × 10−3 | 5.80 × 10−4 | 3.48 × 10−4 | 3.41 × 10−4 | 2.54 × 10−4 | 2.61 × 10−4 |
Fig. 7
Coexistence regime: nutrient availability in heterogeneous domains.
Fig. 8
Coexistence in a fluid at rest.
Fig. 9
Coexistence in a monodirectional fluid.
Fig. 10
Avoiding enemies and predators case, guided by repellent sensitivities.
Fig. 11
Nutrient supply across multiple chemical sources.