Description Usage Arguments Value Examples
This function calculates the vector, gradient, and remainder fields.
1 | VecDecomAll(surface, x.rhs, y.rhs, x.bound, y.bound)
|
surface |
matrix output from |
x.rhs |
a string containing the right hand side of the equation for x. |
y.rhs |
a string containing the right hand side of the equation for y. |
x.bound |
the x boundaries denoted at c(minimum, maximum). |
y.bound |
the y boundaries denoted at c(minimum, maximum). |
returns an array of all three vector fields: the deterministic skeleton, the negative gradient of the quasi-potential, and the remainder. The array has three dimensions with the respective lengths of xstepnumber, ystepnumber, and 6. The six are the x- and y-values for each of the three vector fields, as x-deterministic skeleton, y-deterministic skeleton, x-negative gradient of the quasi-potential, y-negative gradient of the quasi-potential, x-remainder, and y-remainder.
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 31 32 33 34 35 | # First, the 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)
# Sixth, decompose the global quasi-potential into the
# deterministic skeleton, gradient, and remainder vector fields
VDAll <- VecDecomAll(surface = ex1.global, x.rhs = equationx, y.rhs = equationy,
x.bound = xbounds, y.bound = ybounds)
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