Theory and Modern Applications
From: A pest control model with birth pulse and residual and delay effects of pesticides
Birth function | Equilibrium | \(R_{0}\) |
---|---|---|
Ricker | \(x^{*}=\frac{ (1-e^{-q\,dT-\frac{q}{g}(1-e^{-gT})c_{m}-qH} )\ln R^{b}_{0}}{(1-e^{-q(d+\delta )T-\frac{q}{g}(1-e^{-gT})c_{m}-qH}) e^{-q\,dT-\frac{q}{g}(1-e^{-gT})c_{m}-qH}}\) | \(R^{b}_{0}\triangleq \frac{b(1-e^{-q\,dT})e^{-q\,dT-\frac{q}{g}(1-e^{-gT})c_{m}-qH}}{1-e^{-q(d+\delta )T-\frac{q}{g}(1-e^{-gT})c_{m}-qH}}\) \({}\cdot \frac{1}{1-e^{-q\,dT-\frac{q}{g}(1-e^{-gT})c_{m}-qH}}\) |
\(y^{*}=\frac{1-e^{-q\delta T}}{1-e^{-q(d+\delta )T-\frac{q}{g}(1-e^{-gT})c_{m}-qH}}\ln R^{b}_{0}\) | ||
Beverton–Holt | \(x^{*}=\frac{ (1-e^{-q\,dT-\frac{q}{g}(1-e^{-gT})c_{m}-qH} )\sqrt[n]{\beta (R^{p}_{0}-1)}}{(1-e^{-q(d+\delta )T-\frac{q}{g}(1-e^{-gT})c_{m}-qH}) e^{-q\,dT-\frac{q}{g}(1-e^{-gT})c_{m}-qH}}\) | \(R^{p}_{0}\triangleq \frac{p(1-e^{-q\,dT})e^{-q\,dT-\frac{q}{g}(1-e^{-gT})c_{m}-qH}}{\beta (1-e^{-q(d+\delta )T-\frac{q}{g}(1-e^{-gT})c_{m}-qH})}\) \({}\cdot \frac{1}{1-e^{-q\,dT-\frac{q}{g}(1-e^{-gT})c_{m}-qH}}\) |
\(y^{*}=\frac{1-e^{-q\delta T}}{1-e^{-q(d+\delta )T-\frac{q}{g}(1-e^{-gT})c_{m}-qH}}\sqrt[n]{\beta (R^{p}_{0}-1)}\) |