Description Usage Arguments Details Value References See Also Examples
View source: R/grow_genlogistic.R
Generalized logistic growth model solved as differential equation.
1 2 3  ode_genlogistic(time, y, parms, ...)
grow_genlogistic(time, parms, ...)

time 
vector of simulation time steps 
y 
named vector with initial value of the system (e.g. cell concentration) 
parms 
parameters of the generalized logistic growth model

... 
additional parameters passed to the 
The model is given as its first derivative:
dy/dt = mumax * y^alpha * (1(y/K)^beta)^gamma
that is then numerically integrated ('simulated') according to time (t).
The generalized logistic according to Tsoularis (2001) is a flexible model that covers exponential and logistic growth, Richards, Gompertz, von Bertalanffy, and some more as special cases.
The differential equation is solved numerically, where function
ode_genlogistic
is the differential equation, and
grow_genlogistic
runs a numerical simulation over time.
The default version grow_genlogistic
is run directly as compiled code,
whereas the R versions ode_logistic
is
provided for testing by the user.
For ode_genlogistic
: matrix containing the simulation outputs.
The return value of has also class deSolve
.
For grow_genlogistic
: vector of dependent variable (y
).
time
time of the simulation
y
abundance of organisms
Tsoularis, A. (2001) Analysis of Logistic Growth Models. Res. Lett. Inf. Math. Sci, (2001) 2, 2346.
Other growth models:
grow_baranyi()
,
grow_exponential()
,
grow_gompertz2()
,
grow_gompertz()
,
grow_huang()
,
grow_logistic()
,
grow_richards()
,
growthmodel
,
ode_twostep()
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16  time < seq(0, 30, length=200)
parms < c(mumax=0.5, K=10, alpha=1, beta=1, gamma=1)
y0 < c(y=.1)
out < ode(y0, time, ode_genlogistic, parms)
plot(out)
out2 < ode(y0, time, ode_genlogistic, parms = c(mumax=0.2, K=10, alpha=2, beta=1, gamma=1))
out3 < ode(y0, time, ode_genlogistic, parms = c(mumax=0.2, K=10, alpha=1, beta=2, gamma=1))
out4 < ode(y0, time, ode_genlogistic, parms = c(mumax=0.2, K=10, alpha=1, beta=1, gamma=2))
out5 < ode(y0, time, ode_genlogistic, parms = c(mumax=0.2, K=10, alpha=.5, beta=1, gamma=1))
out6 < ode(y0, time, ode_genlogistic, parms = c(mumax=0.2, K=10, alpha=1, beta=.5, gamma=1))
out7 < ode(y0, time, ode_genlogistic, parms = c(mumax=0.3, K=10, alpha=1, beta=1, gamma=.5))
plot(out, out2, out3, out4, out5, out6, out7)
## growth with lag (cf. log_y)
plot(ode(y0, time, ode_genlogistic, parms = c(mumax=1, K=10, alpha=2, beta=.8, gamma=5)))

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