This function calculates the remainder field.

1 | ```
VecDecomRem(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 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.

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)
``` |

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