Theory and Modern Applications
Table 1 Variables and parameters used in the model
From: Threshold dynamics of a predator–prey model with age-structured prey
Symbol | Definition |
|---|---|
\(U_{1}(t)\) | number of juvenile prey at time t |
\(U_{2}(t)\) | number of mature prey at time t |
P(t) | number of the predator at time t |
\(u_{1}(t,a)\) | density of the juvenile prey at time t of age a |
\(u_{2}(t,a)\) | density of the mature prey at time t of age a |
\(\mu_{2}\) | per capita mortality rate of mature prey |
\(\mu_{1}\) | per capita mortality rate of juvenile prey |
\(\mu_{P}\) | per capita mortality rate for the predator |
\(c_{1}\) | prey juvenile biomass encounter rate |
\(c_{2}\) | prey adult biomass encounter rate |
β | the age-specific fertility rate or birth rate |
h(a) | the handling (digestion) time per unit biomass consumed |
\(m_{1}\) | the per capita capture rate of juvenile prey by a searching predator |
\(m_{2}\) | the per capita capture rate of mature prey by a searching predator |
τ | maturation time of juvenile prey |
u(t,0) | egg laying rate of mature prey |
θ | maximum per capita female egg release |
\(f(U_{2})\) | the effects of the predation on the fertility of mature prey: \((\theta U_{2})/(1+\theta U_{2})\) |