QPot (version 1.0)

VecDecomPlot: Plotting function for vector decomposition and remainder fields

Description

This function calculates the vector and remainder fields.

Usage

VecDecomPlot(field, dens, x.bound, y.bound, xlim = "NULL", ylim = "NULL",
  arrow.type = "equal", tail.length = 0.25, head.length = 0.25, ...)

Arguments

field

list output from VecDecomAll, VecDecomVec, VecDecomGrad, or

dens

two-element vector respectively specifying the number of respective arrows in the x and y directions.

x.bound

two-element vector for the x domain boundries used for the quasi-potential simulation.

y.bound

two-element vector for the y domain boundries used for the quasi-potential simulation.

xlim

numeric vectors of length 2, giving the x coordinate range.

ylim

numeric vectors of length 2, giving the y coordinate range.

arrow.type

sets the type of line segments plotted. If set to "proportional" the length of the line segments reflects the magnitude of the derivative. If set to "equal" the line segments take equal lengths, simply reflecting the gradient of the derivative(s). Default

tail.length

multiplies the current length of the tail (both proportional and equal arrow.types) by the specified factor. The argument defaults to 1, which is length of the longest vector within the domain boundaries (i.e., the entire field).

head.length

THIS NEEDS WORDS

...

passes arguments to both plot and arrows.

Examples

# 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)

# 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)

# Seventh, plot all three vector fields
	# The deterministic skeleton vector field
	VecDecomPlot(field = list(VDAll[,,1], VDAll[,,2]), dens = c(25,25),
		x.bound = xbounds, y.bound = ybounds, tail.length = 0.75, head.length = 0.05)
	# The gradient vector field
	VecDecomPlot(field = list(VDAll[,,3], VDAll[,,4]), dens = c(25,25),
		x.bound = xbounds, y.bound = ybounds, tail.length = 0.15, head.length = 0.05)
	# The remainder vector field
	VecDecomPlot(field = list(VDAll[,,5], VDAll[,,6]), dens = c(25,25),
		x.bound = xbounds, y.bound = ybounds, tail.length = 0.15, head.length = 0.05)