Theory and Modern Applications
Table 1 Description of model parameters
\(g_{0}\) | Intrinsic growth rate |
\(\beta _{10}\) | Dissolved oxygen’s minimum natural concentration needed by the aquatic species |
\(\beta _{11}\) | Increment rate in the mass of mixed oxygen demanded for the species per unit rise in the level of temperature above the suitable temperature |
\(T_{\mathrm{opt}}\) | Optimal water temperature for the aquatic species maximum rate of growth |
\(\gamma _{0}\) | Carrying capacity of the environment |
\(D_{s_{0}}\) | Dissolved oxygen’s natural saturated concentration at \(T = T_{\mathrm{opt}}\) |
\(A_{0}\) | Ejection rate of greenhouse gases cause of anthropogenic bustles |
w | Increment rate in the temperature of water cause of greenhouse gases |
\(\zeta _{1}\) | Coefficient of heat transfer of surface |
\(O_{c}\) | Physic manufacture of concentration of ozone per unit time in the environment |
\(\Lambda _{1}\) | Natural deterioration rate of concentration of ozone |
Λ | Deterioration rate of concentration of ozone cause of greenhouse gases |
\(\gamma _{1}\) | Coefficient of reaeration at the reference temperature |
\(\delta _{2}\) | Deterioration rate of mixed oxygen because of breathing by the species |
ζ | Deterioration rate of mixed oxygen because of a rise in the temperature above the suitable temperature |
β | A constant that succumbs upon the tincture state of the water body |
γ | Variations rate in the water temperature because of changes in the ozone concentration level associated with its threshold value |
\(Z_{0}\) | Threshold of concentration of ozone below which temperature will rise |
\(T_{10}\) | Temperature of the environment |
\(\delta _{1}\) | Depletion rate of greenhouse gases |
\(T_{0}\) | Context temperature (associated with the turbulence degree in the water, in which turn succumbs on the depth and speed of the river) |
b | Constant that incarnates the toxic influence of divergence of T from \(T_{\mathrm{opt}}\) and divergence of T from \(T_{\max }\) |
\(T_{\max }\) | Maximum temperature of water at which growth can occur |
N(0) | Initial population of N |
T(0) | Initial population of T |
C(0) | Initial population of C |
Z(0) | Initial population of Z |
U(0) | Initial population of U |