Description Usage Arguments Examples
This function allows you to find the global quasi-potential values for several local quasi-potential surfaces
1 | QPGlobal(local.surfaces, unstable.eq.x, unstable.eq.y, x.bound, y.bound)
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local.surfaces |
a list of local quasi-potential surfaces, each of which is stored in discretized form as a matrix. |
unstable.eq.x |
a vector of the x-coordinates of the unstable equilibria. Must be in the same order as unstable.eq.y. |
unstable.eq.y |
a vector of the y-coordinates of the unstable equilibria. Must be in the same order as unstable.eq.x. |
x.bound |
a two-element vector with the minimum and maximum x values used for computing the quasi-potential. |
y.bound |
a two-element vector with the minimum and maximum y values used for computing the quasi-potential. |
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 | # First, System of equations
equationx <- "1.54*x*(1.0-(x/10.14)) - (y*x*x)/(1.0+x*x)"
equationy <- "((0.476*x*x*y)/(1+x*x)) - 0.112590*y*y"
# Second, shared parameters for each quasi-potential run
xbounds <- c(-0.5, 10.0)
ybounds <- c(-0.5, 10.0)
xstepnumber <- 100
ystepnumber <- 100
# Third, first local quasi-potential run
xinit1 <- 1.40491
yinit1 <- 2.80808
storage.eq1 <- QPotential(x.rhs = equationx, x.start = xinit1,
x.bound = xbounds, x.num.steps = xstepnumber, y.rhs = equationy,
y.start = yinit1, y.bound = ybounds, y.num.steps = ystepnumber)
# Fourth, second local quasi-potential run
xinit2 <- 4.9040
yinit2 <- 4.06187
storage.eq2 <- QPotential(x.rhs = equationx, x.start = xinit2,
x.bound = xbounds, x.num.steps = xstepnumber, y.rhs = equationy,
y.start = yinit2, y.bound = ybounds, y.num.steps = ystepnumber)
# Fifth, determine global quasi-potential
unst.x <- c(0, 4.2008)
unst.y <- c(0, 4.0039)
ex1.global <- QPGlobal(local.surfaces = list(storage.eq1, storage.eq2),
unstable.eq.x = unst.x, unstable.eq.y = unst.y, x.bound = xbounds,
y.bound = ybounds)
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