View source: R/grow_genlogistic.R
ode_genlogistic | R Documentation |
Generalized logistic growth model solved as differential equation.
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, 23-46.
Other growth models:
grow_baranyi()
,
grow_exponential()
,
grow_gompertz2()
,
grow_gompertz()
,
grow_huang()
,
grow_logistic()
,
grow_richards()
,
growthmodel
,
ode_twostep()
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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