Table 1 Parameter definitions in systems ( 1.2 )-( 1.3 ) and their units, where \(\pmb{[\mathrm{species}\ u]}\) indicates the species u density and \(\pmb{[\mathrm{species}\ v]}\) indicates species v density
Symbol | Parameter definition | Units |
|---|---|---|
\(r_{1}\) | Species u intrinsic growth rate | 1/time |
\(r_{2}\) | Species v intrinsic growth rate | 1/time |
\(c_{1}\) | Half-saturation density constant of species u | [species u] |
\(c_{2}\) | Half-saturation density constant of species v | [species v] |
\(\alpha_{12}\) | Resource consumption rate of species u | 1/time |
\(\beta_{1}\) | Resource supplying rate of species u | \([\mathrm{species}\ v]^{-1}(1/\mathrm{time})\) |
\(\alpha_{21}\) | Resource consumption rate of species v | 1/time |
\(r_{1}/d_{1}\) | Species u carrying capacity | [species u] |
\(r_{2}/d_{2}\) | Species v carrying capacity | [species v] |
\(a_{1}\) | Self-diffusion coefficient of species u | \((\mathrm{distance})^{2}(1/\mathrm{time})\) |
\(a_{2}\) | Self-diffusion coefficient of species v | \((\mathrm{distance})^{2}(1/\mathrm{time}) \) |
b | Cross-diffusion coefficient of species v | \((\mathrm{distance})^{2}(1/\mathrm{time})[\mathrm{species}\ u]^{-1}\) |