Description Usage Format See Also
The lvaproxdata
provides the data in LV
dataset to simulate prey-predator (Lotka-Volterra) model. The original code was written by Joshua Abbott in MATLAB and Seong Do Yun adapted it to a package example. The prey-predator model is:
Prey (X): \dot{X} = rX ≤ft( 1 - \frac{X}{K} \right) - aXY - θ X , and
Predator (Y): \dot{Y} = bXY - mY - γ Y .
The parameters are given as:
r = 0.025: intrinsic growth rate for prey,
K = 1: carrying capacity for prey,
a = 0.08: predator-related mortality parameter for prey,
b = 0.05: predator/prey uptake parameter for predator,
m = 0.01: natural mortality for predator,
γ = 0.005: slope for linear predator harvest control rule, and
θ = 0.005: slope for linear prey harvest control rule
The predator with no economic value (unharvested) is designed for the economic program as:
W = harv.prey(p.prey-c.prey/X)θ X + harv.pred*(p.pred-c.pred/Y)γ Y.
The paramters are:
p.pred = 0: price per unit harvest of predator,
p.prey = 25: price per unit harvest of prey,
c.prey = 0.1 p_prey: cost /per unit of prey effort in Schaefer model (really c/q with q=1), and
c.pred = c_prey: cost per unit of predator effort in Schaefer model (really c/q with q=1).
1 2 | ## Load dataset
data("lvdata")
|
lvaproxdata: a data.frame for approximation (evaluated on (20 x 20) Chebyshev nodes)
xs
prey stock
ys
predator stock
xdot
evaluated xdot \frac{dx}{dt}
ydot
evaluated ydot \frac{dy}{dt}
wval
profit (W in Fenichel and Abtott (2014))
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