eode_is_stapoi {ecode}

Stable Equilibrium Point

Description

Check whether an equilibrium point is stable or not.

Usage

eode_is_stapoi(x, value, eps = 0.001)

Arguments

x

Object of class "eode" representing an ODE system.

value

an object of class "pp" representing a phase point in the ODE system under consideration.

eps

Precision used to check whether the input phase point is an equilibrium point. If the absolute value of any component of the phase velocity vector at a phase point is lower than eps, an error would be thrown out.

Value

a TRUE or FALSE.

Examples

eq1 <- function(x, y, r1 = 1, a11 = 1, a12 = 2) (r1 - a11 * x - a12 * y) * x
eq2 <- function(x, y, r2 = 1, a21 = 2, a22 = 1) (r2 - a21 * x - a22 * y) * y
x <- eode(dxdt = eq1, dydt = eq2)
eode_is_stapoi(x, value = pp(list(x = 0.3333, y = 0.3333)))

## Example2: Susceptible-infected model
dX_Cdt <- function(X_C, Y_C, X_A, Y_A, nu = 0.15, beta = 0.1, mu = 0.15, g = 0.04) {
  nu * (X_A + Y_A) - beta * X_C * (Y_C + Y_A) - (mu + g) * X_C
}

dY_Cdt <- function(X_C, Y_C, Y_A, beta = 0.1, mu = 0.15, g = 0.04, rho = 0.2) {
  beta * X_C * (Y_C + Y_A) - (mu + g + rho) * Y_C
}

dX_Adt <- function(X_C, Y_C, X_A, Y_A, beta = 0.1, g = 0.04) {
  g * X_C - beta * X_A * (Y_C + Y_A)
}

dY_Adt <- function(X_A, Y_C, Y_A, beta = 0.1, g = 0.04, rho = 0.2) {
  beta * X_A * (Y_C + Y_A) + g * Y_C - rho * Y_A
}

x <- eode(
  dX_Cdt = dX_Cdt, dY_Cdt = dY_Cdt, dX_Adt = dX_Adt, dY_Adt = dY_Adt,
  constraint = c(
    "X_C>=0", "Y_C>=0", "X_A>=0", "Y_A>=0",
    "X_C<5", "Y_C<5", "X_A<5", "Y_A<5"
  )
)
eode_is_stapoi(x, value = pp(list(X_A = 1.3443, Y_A = 0.2304, X_C = 1.0655, Y_C = 0.0866)))