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###############################################
## Soetaert and Herman (2008) ##
## A practical guide to ecological modelling ##
## Chapter 7. ##
## Stability and steady-state ##
## Chapter 7.8.3 ##
## The Lorenz equations-chaos ##
###############################################
# package with the integration and 3-d plotting routine:
require(deSolve)
require(scatterplot3d)
#----------------------#
# the model equations: #
#----------------------#
Lorenz<-function(t,state,parameters)
{
with(as.list(c(state)),{
## the rates of change of state variables
dx <- -8/3*x+y*z
dy <- -10*(y-z)
dz <- -x*y+28*y-z
## the output
list(c(dx,dy,dz)) })
} # end of model
#-------------------------#
# the initial conditions: #
#-------------------------#
state <-c(x=1,
y=1,
z=1)
#----------------------#
# RUNNING the model: #
#----------------------#
times <-seq(0,100,0.001)
out <-as.data.frame(vode(state,times,Lorenz,0))
#------------------------#
# PLOTTING model output: #
#------------------------#
#windows()
#par(mfrow=c(2,2),oma=c(1,2,2,2))
#plot (out$y,out$x,type="l")
#plot (out$y,out$z,type="l")
#plot (out$z,out$x,type="l")
#plot (out$time,out$x,type="l")
#mtext(outer=TRUE,side=3,"Lorenz butterfly",line=-1)
windows()
scatterplot3d(out$x,out$y,out$z,type="l",main="Lorenz butterfly",ylab="",
grid=FALSE,box=FALSE)
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