VecDecomGrad: Vector decomposition and remainder fields

In QPot: Quasi-Potential Analysis for Stochastic Differential Equations

Description

This function calculates the gradient field.

Usage

VecDecomGrad(surface)

Arguments

surface

matrix output from QPGlobal or QPotential.

Value

returns an array of the gradient vector field. The array has three dimensions with the respective lengths of the columns of the surface, the rows of the sruface, and the number of variables (always 2). The two variables are the x-negative gradient of the quasi-potential surface and the y-negative gradient of the quasi-potential surface.

Examples

# 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, creat the gradient vector field
	VDG <- VecDecomGrad(surface = ex1.global)

QPot documentation built on May 2, 2019, 2:34 p.m.