Nothing
## ----setup, include = FALSE---------------------------------------------------
knitr::opts_chunk$set(
collapse = TRUE,
comment = "#>"
)
## ---- echo = F----------------------------------------------------------------
suppressPackageStartupMessages(library(phaseR))
## ---- echo = F, fig.dim = c(7, 5)---------------------------------------------
example1_flowField <- flowField(example1,
xlim = c(0, 10),
ylim = c(-5, 5),
system = "one.dim",
add = F)
example1_trajectories <- trajectory(example1,
y0 = c(-4, -1, 1, 4),
tlim = c(0, 10),
system = "one.dim",
col = rep("black", 4),
add = T)
## ---- echo = F, fig.dim = c(7, 5)---------------------------------------------
example1_phasePortrait <- phasePortrait(example1,
ylim = c(-5, 5))
## ---- echo = F, fig.dim = c(7, 5)---------------------------------------------
lotkaVolterra_flowField <- flowField(lotkaVolterra,
xlim = c(0, 5),
ylim = c(0, 5),
parameters = c(1, 1, 1, 1),
add = F)
lotkaVolterra_trajectories <- trajectory(lotkaVolterra,
y0 = rbind(c(2, 2),
c(0.5, 0.5),
c(0.5, 1.5),
c(1.5, 0.5),
c(3, 3)),
parameters = c(1, 1, 1, 1),
col = rep("black", 5),
tlim = c(0, 100))
## ---- echo = F, fig.dim = c(7, 5)---------------------------------------------
lotkaVolterra_flowField <- flowField(lotkaVolterra,
xlim = c(0, 5),
ylim = c(0, 5),
parameters = c(1, 1, 1, 1),
add = F)
lotkaVolterra_trajectories <- nullclines(lotkaVolterra,
xlim = c(-0.5, 5),
ylim = c(-0.5, 5),
parameters = c(1, 1, 1, 1),
points = 251)
## ---- echo = F, fig.dim = c(7, 5)---------------------------------------------
lotkaVolterra_numericalSolution <- numericalSolution(lotkaVolterra,
y0 = c(3, 4),
tlim = c(0, 50),
parameters = c(1, 1, 1, 1))
## ---- eval = F----------------------------------------------------------------
# drawManifolds(deriv, y0 = NULL, parameters = NULL, tstep = 0.1, tend = 1000,
# col = c("green", "red"), add.legend = TRUE,
# state.names = c("x", "y"), ...)
## ---- eval = F----------------------------------------------------------------
# findEquilibrium(deriv, y0 = NULL, parameters = NULL, system = "two.dim",
# tol = 1e-16, max.iter = 50, h = 1e-6, plot.it = FALSE,
# summary = TRUE,
# state.names = if (system == "two.dim") c("x", "y") else "y")
## ---- eval = F----------------------------------------------------------------
# flowField(deriv, xlim, ylim, parameters = NULL, system = "two.dim", points = 21,
# col = "gray", arrow.type = "equal", arrow.head = 0.05, frac = 1,
# add = TRUE,
# state.names = if (system == "two.dim") c("x", "y") else "y",
# xlab = if (system == "two.dim") state.names[1] else "t",
# ylab = if (system == "two.dim") state.names[2] else state.names[1],
# ...)
## ---- eval = F----------------------------------------------------------------
# nullclines(deriv, xlim, ylim, parameters = NULL, system = "two.dim",
# points = 101, col = c("blue", "cyan"), add = TRUE, add.legend = TRUE,
# state.names = if(system == "two.dim") c("x", "y") else "y", ...)
## ---- eval = F----------------------------------------------------------------
# numericalSolution(deriv, y0 = NULL, tlim, tstep = 0.01, parameters = NULL,
# type = "one", col = c("red", "blue"), add.grid = TRUE,
# add.legend = TRUE, state.names = c("x", "y"), xlab = "t",
# ylab = state.names)
## ---- eval = F----------------------------------------------------------------
# phasePlaneAnalysis(deriv, xlim, ylim, tend = 100, parameters = NULL,
# system = "two.dim", add = FALSE,
# state.names = if (system == "two.dim") c("x", "y") else "y")
## ---- eval = F----------------------------------------------------------------
# phasePortrait(deriv, ylim, ystep = 0.01, parameters = NULL, points = 10,
# frac = 0.75, arrow.head = 0.075, col = "black", add.grid = TRUE,
# state.names = "y", xlab = state.names,
# ylab = paste0("d", state.names), ...)
## ---- eval = F----------------------------------------------------------------
# stability(deriv, ystar = NULL, parameters = NULL, system = "two.dim", h = 1e-07,
# summary = TRUE,
# state.names = if (system == "two.dim") c("x", "y") else "y")
## ---- eval = F----------------------------------------------------------------
# trajectory(deriv, y0 = NULL, n = NULL, tlim, tstep = 0.01, parameters = NULL,
# system = "two.dim", col = "black", add = TRUE,
# state.names = if (system == "two.dim") c("x", "y") else "y", ...)
## ---- eval = F----------------------------------------------------------------
# derivative <- function(t, y, parameters) {
# # Enter derivative computation here
# list(dy)
# }
## ---- eval = F----------------------------------------------------------------
# derivative <- function(t, y, parameters) {
# x <- y[1]
# y <- y[2]
# dy <- c(3*y, 2*x)
# list(dy)
# }
## ---- eval = F----------------------------------------------------------------
# derivative <- function(t, y, parameters) {
# alpha <- parameters[1]
# beta <- parameters[2]
# x <- y[1]
# y <- y[2]
# dy <- c(alpha*y, beta*x)
# list(dy)
# }
## ---- eval = F----------------------------------------------------------------
# derivative <- function(t, y, parameters) {
# a <- parameters[1]
# b <- parameters[2]
# dy <- a*(b – 3 - y)^2
# list(dy)
# }
## ---- echo = T, fig.dim = c(7, 5)---------------------------------------------
example2_flowField <- flowField(example2,
xlim = c(0, 4),
ylim = c(-1, 3),
system = "one.dim",
add = FALSE)
grid()
example2_nullclines <- nullclines(example2,
xlim = c(0, 4),
ylim = c(-1, 3),
system = "one.dim")
example2_trajectory <- trajectory(example2,
y0 = c(-0.5, 0.5, 1.5, 2.5),
tlim = c(0, 4),
system = "one.dim")
## ---- echo = T, fig.dim = c(7, 5)---------------------------------------------
example2_phasePortrait <- phasePortrait(example2,
ylim = c(-0.5, 2.5))
## ---- echo = T----------------------------------------------------------------
example2_stability_1 <- stability(example2,
ystar = 0,
system = "one.dim")
example2_stability_2 <- stability(example2,
ystar = 1,
system = "one.dim")
example2_stability_3 <- stability(example2,
ystar = 2,
system = "one.dim")
## ---- echo = T, fig.dim = c(7, 5)---------------------------------------------
logistic_flowField <- flowField(logistic,
xlim = c(0, 5),
ylim = c(-1, 3),
parameters = c(1, 2),
system = "one.dim",
add = FALSE)
grid()
logistic_nullclines <- nullclines(logistic,
xlim = c(0, 5),
ylim = c(-1, 3),
parameters = c(1, 2),
system = "one.dim")
logistic_trajectory <- trajectory(logistic,
y0 = c(-0.5, 0.5, 1.5, 2.5),
tlim = c(0, 5),
parameters = c(1, 2),
system = "one.dim")
## ---- echo = T, fig.dim = c(7, 5)---------------------------------------------
logistic_phasePortrait <- phasePortrait(logistic,
ylim = c(-0.5, 2.5),
parameters = c(1, 2))
## ---- echo = T----------------------------------------------------------------
logistic_stability_1 <- stability(logistic,
ystar = 0,
parameters = c(1, 2),
system = "one.dim")
logistic_stability_2 <- stability(logistic,
ystar = 2,
parameters = c(1, 2),
system = "one.dim")
## ---- echo = T, fig.dim = c(7, 5)---------------------------------------------
example4_flowField <- flowField(example4,
xlim = c(-3, 3),
ylim = c(-5, 5),
add = FALSE)
grid()
example4_nullclines <- nullclines(example4,
xlim = c(-3, 3),
ylim = c(-5, 5))
y0 <- matrix(c(1, 0, -1, 0, 2, 2, -2, 2, 3, -3, -3, -4),
6, 2, byrow = TRUE)
example4_trajectory <- trajectory(example4,
y0 = y0,
tlim = c(0, 10))
## ---- echo = T, fig.dim = c(7, 5)---------------------------------------------
example5_flowField <- flowField(example5,
xlim = c(-3, 3),
ylim = c(-3, 3),
add = FALSE)
grid()
example5_nullclines <- nullclines(example5,
xlim = c(-3, 3),
ylim = c(-3, 3))
y0 <- matrix(c(1, 0, -1, 0, 2, 2, -2, 2, 0, 3, 0, -3),
6, 2, byrow = TRUE)
example5_trajectory <- trajectory(example5,
y0 = y0,
tlim = c(0, 10))
example5_manifolds <- drawManifolds(example5,
y0 = c(0, 0))
## ---- echo = T----------------------------------------------------------------
example5_stability <- stability(example5,
ystar = c(0, 0))
## ---- echo = T, fig.dim = c(7, 5)---------------------------------------------
example8_flowField <- flowField(example8,
xlim = c(-3, 3),
ylim = c(-3, 3),
add = FALSE)
grid()
example8_nullclines <- nullclines(example8,
xlim = c(-3, 3),
ylim = c(-3, 3))
y0 <- matrix(c(1, 0, 0, 0.5, 2, -2, -2, -2),
4, 2, byrow = TRUE)
example8_trajectory <- trajectory(example8,
y0 = y0,
tlim = c(0, 10))
## ---- echo = T----------------------------------------------------------------
example8_stability <- stability(example8,
ystar = c(0, 0))
## ---- echo = T, fig.dim = c(7, 5)---------------------------------------------
example11_flowField <- flowField(example11,
xlim = c(-5, 5),
ylim = c(-5, 5),
add = FALSE)
grid()
example11_nullclines <- nullclines(example11,
xlim = c(-5, 5),
ylim = c(-5, 5),
points = 500)
y0 <- matrix(c(4, 4, -1, -1, -2, 1, 1, -1),
4, 2, byrow = TRUE)
example11_trajectory <- trajectory(example11,
y0 = y0,
tlim = c(0, 10))
## ---- echo = T----------------------------------------------------------------
example11_stability_1 <- stability(example11,
ystar = c(0, 0))
example11_stability_2 <- stability(example11,
ystar = c(0, 2))
example11_stability_3 <- stability(example11,
ystar = c(1, 1),
h = 1e-8)
example11_stability_4 <- stability(example11,
ystar = c(3, 0))
## ---- echo = T, fig.dim = c(7, 5)---------------------------------------------
example12_flowField <- flowField(example12,
xlim = c(-4, 4),
ylim = c(-4, 4),
add = FALSE)
grid()
example12_nullclines <- nullclines(example12,
xlim = c(-4, 4),
ylim = c(-4, 4),
points = 500)
y0 <- matrix(c(2, 2, -3, 0, 0, 2, 0, -3),
4, 2, byrow = TRUE)
example12_trajectory <- trajectory(example12,
y0 = y0,
tlim = c(0, 10))
## ---- echo = T----------------------------------------------------------------
example12_stability_1 <- stability(example12,
ystar = c(1, 1))
example12_stability_2 <- stability(example12,
ystar = c(-1, -1),
h = 1e-8)
## ---- echo = T, fig.dim = c(7, 5)---------------------------------------------
simplePendulum_flowField <- flowField(simplePendulum,
xlim = c(-7, 7),
ylim = c(-7, 7),
parameters = 5,
add = FALSE)
grid()
simplePendulum_nullclines <- nullclines(simplePendulum,
xlim = c(-7, 7),
ylim = c(-7, 7),
parameters = 5,
points = 500)
y0 <- matrix(c(0, 1, 0, 4, -6, 1, 5, 0.5, 0, -3),
5, 2, byrow = TRUE)
simplePendulum_trajectory <- trajectory(simplePendulum,
y0 = y0,
tlim = c(0, 10),
parameters = 5)
## ---- echo = T, fig.dim = c(7, 5)---------------------------------------------
simplePendulum_stability_1 <- stability(simplePendulum,
ystar = c(0, 0),
parameters = 5)
simplePendulum_stability_2 <- stability(simplePendulum,
ystar = c(pi, 0),
parameters = 5)
## ---- echo = T----------------------------------------------------------------
vanDerPol_stability_1 <- stability(vanDerPol, ystar = c(0, 0),
parameters = 3)
vanDerPol_stability_2 <- stability(vanDerPol, ystar = c(0, 0),
parameters = 1)
## ---- echo = T, fig.dim = c(7, 5)---------------------------------------------
vanDerPol_flowField <- flowField(vanDerPol,
xlim = c(-5, 5),
ylim = c(-5, 5),
parameters = 3,
add = FALSE)
grid()
vanDerPol_nullclines <- nullclines(vanDerPol,
xlim = c(-5, 5),
ylim = c(-5, 5),
parameters = 3,
points = 500)
y0 <- matrix(c(2, 0, 0, 2, 0.5, 0.5),
3, 2, byrow = TRUE)
vanDerPol_trajectory <- trajectory(vanDerPol,
y0 = y0,
tlim = c(0, 10),
parameters = 3)
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