Nothing
set.seed(1) knitr::opts_chunk$set(fig.width = 8, fig.height = 6)
This version of the Lotka predator-prey model is given by
dY1/dt = c1*Y1 - c2*Y1*Y2 dY2/dt = c2*Y1*Y2 - c3*Y2
consisting of the three reaction channels,
Y1 --c1--> Y1 + Y1 Y1 + Y2 --c2--> Y2 + Y2 Y1 --c3--> 0
Load package
library(GillespieSSA)
Define parameters
parms <- c(c1 = 10, c2 = .01, c3 = 10) tf <- 2 # Final time simName <- "Lotka predator-prey model" # Name
Define initial state vector
x0 <- c(Y1=1000, Y2=1000)
Define state-change matrix
nu <- matrix(c(+1, -1, 0, 0, 1, -1), nrow = 2, byrow = TRUE)
Define propensity functions
a <- c("c1*Y1", "c2*Y1*Y2","c3*Y2")
Run simulations with the Direct method
set.seed(1) out <- ssa( x0 = x0, a = a, nu = nu, parms = parms, tf = tf, method = ssa.d(), simName = simName, verbose = FALSE, consoleInterval = 1 ) ssa.plot(out, show.title = TRUE, show.legend = FALSE)
Run simulations with the Explict tau-leap method
set.seed(1) out <- ssa( x0 = x0, a = a, nu = nu, parms = parms, tf = tf, method = ssa.etl(tau = .002), simName = simName, verbose = FALSE, consoleInterval = 1 ) ssa.plot(out, show.title = TRUE, show.legend = FALSE)
Run simulations with the Binomial tau-leap method
set.seed(1) out <- ssa( x0 = x0, a = a, nu = nu, parms = parms, tf = tf, method = ssa.btl(f = 100), simName = simName, verbose = FALSE, consoleInterval = 1 ) ssa.plot(out, show.title = TRUE, show.legend = FALSE)
Run simulations with the Optimized tau-leap method
set.seed(1) out <- ssa( x0 = x0, a = a, nu = nu, parms = parms, tf = tf, method = ssa.otl(epsilon = .1), simName = simName, verbose = FALSE, consoleInterval = 1 ) ssa.plot(out, show.title = TRUE, show.legend = FALSE)
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