QPot (version 1.5)

TSTraj: Simulate two-dimensional stochastic differential equations

Description

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

Usage

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

Arguments

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 \(\Delta t\).

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.

Value

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

Examples

# NOT RUN {
# 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)
# }