TSTraj: Simulate two-dimensional stochastic differential equations
In bmarkslash7/QPot: Quasi-Potential Analysis for Stochastic Differential Equations

Description Usage Arguments Value Examples

This function allows you to simulate two-dimensional stochastic differential equations.

TSTraj(
  init.x = NULL,
  init.y = NULL,
  y0 = NULL,
  time,
  deltat,
  x.rhs,
  y.rhs,
  parms = NA,
  sigma,
  lower.bound = NA,
  upper.bound = NA
)

`init.x`	initial condition for the x state variable
`init.y`	initial condition for the y state variable
`y0`	instead of init.x and init.y, can assign a two-element vector of the initial conditions for the state variables. Elements must be assigned as objects (see Example below).
`time`	numeric value indicating the total time over which the simulation is to be run.
`deltat`	numeric value indicating the frequency of stochastic perturbation, as Δ t.
`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.
`parms`	n-element vector of objects representing unvalued parameters in the equation. If parameter values are values in the equation, then default is `parms = NA`.
`sigma`	numeric value specifying the noise intensity.
`lower.bound`	numeric value specifying a lower bound in the simulation.
`upper.bound`	numeric value specifying an upper bound in the simulation.

returns a matrix with three columns (timestep, x values, and y values) with a length of time/deltat (2*e4 in the examples below).

# First, the parameter values
model.state <- c(x = 3, y = 3)
model.sigma <- 0.2
model.deltat <- 0.1
model.time <- 100

# Second, write out the deterministic skeleton of the equations to be simulated
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"

# Third, Run it
ModelOut <- TSTraj(y0 = model.state, time = model.time, deltat = model.deltat, 
	x.rhs = equationx, y.rhs = equationy, sigma = model.sigma)

# Can also input x.rhs and y.rhs as strings that contain parameter names 
# and include parms with names and values of parameters
model.state <- c(x = 1, y = 2)
model.parms <- c(alpha = 1.54, beta = 10.14, delta = 1, kappa = 1, gamma = 0.476, mu = 0.112509)
model.sigma <- 0.2
model.time <- 100
model.deltat <- 0.1

test.eqn.x = "(alpha*x)*(1-(x/beta)) - ((delta*(x^2)*y)/(kappa + (x^2)))"
test.eqn.y = "((gamma*(x^2)*y)/(kappa + (x^2))) - mu*(y^2)"

ModelOut.parms <- TSTraj(y0 = model.state, time = model.time, deltat = model.deltat, 
	x.rhs = test.eqn.x, y.rhs = test.eqn.y, parms = model.parms, sigma = model.sigma)