# VecDecomRem: Vector decomposition and remainder fields In QPot: Quasi-Potential Analysis for Stochastic Differential Equations

## Description

This function calculates the remainder field.

## Usage

 `1` ```VecDecomRem(surface, x.rhs, y.rhs, x.bound, y.bound) ```

## Arguments

 `surface` matrix output from `QPGlobal` or `QPotential`. `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).

## Value

returns an array of the remainder 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-remainder and y-remainder.

## Examples

 ``` 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``` ```# 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 <- 150 ystepnumber <- 150 # 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, create remainder field VDR <- VecDecomRem(surface = ex1.global, x.rhs = equationx, y.rhs = equationy, x.bound = xbounds, y.bound = ybounds) ```

QPot documentation built on May 29, 2017, 8:01 p.m.